Exercises on algebraic expressions

Algebraic expressions are expressions that bring together letters, called variables, numbers and mathematical operations.

Test your knowledge with the 10 questions that we created on the topic and answer your questions with the comments in the resolutions.

question 1

Solve the algebraic expression and complete the table below.

x	2		5
3x - 4		5		20

Based on your calculations, the values ​​of , , and are, respectively:

a) 2, 3, 11 and 8
b) 4, 6, 13 and 9
c) 1, 5, 17 and 8
d) 3, 1, 15 and 7

See Answer

Correct alternative: a) 2, 3, 11 and 8.

To complete the picture we must substitute the value of x in the expression when its value is given and solve the expression with the presented result to find the value of x.

For x = 2:

3.2 - 4 = 6 - 4 = 2

Therefore, = 2

For 3x - 4 = 5:

3x - 4 = 5
3x = 5 + 4
3x = 9
x = 9/3
x = 3

Therefore, = 3

For x = 5:

3.5 - 4 = 15 - 4 = 11

Therefore, = 11

For 3x - 4 = 20:

3x - 4 = 20
3x = 20 + 4
3x = 24
x = 24/3
x = 8

Therefore, = 8

Therefore, the symbols are replaced, respectively, by the numbers 2, 3, 11 and 8, according to alternative a).

question 2

What is the value of the algebraic expression for a = 2, b = - 5 and c = 2?

to 1
b) 2
c) 3
d) 4

See Answer

Correct alternative: c) 3.

To find the numeric value of the expression we must replace the variables with the values ​​given in the question.

Where a = 2, b = - 5 and c = 2, we have:

Therefore, when a = 2, b = - 5 and c = 2, the numeric value of the expression is 3 as per alternative c).

question 3

What is the numeric value of the expression for x = - 3 and y = 7?

a) 6
b) 8
c) -8
d) -6

See Answer

Correct alternative: d) -6.

If x = - 3 and y = 7, then the numeric value of the expression is:

Therefore, alternative d) is correct, because when x = - 3 and y = 7 the algebraic expression has numerical value - 6.

question 4

If Pedro is x years old, which expression determines the triple of his age in 6 years?

a) 3x + 6
b) 3(x + 6)
c) 3x + 6x
d) 3x.6

See Answer

Correct alternative: b) 3(x + 6).

If Peter's age is x, then in 6 years Peter will be age x + 6.

To determine the algebraic expression that calculates the triple of your age in 6 years, we must multiply by 3 the age x + 6, that is, 3(x + 6).

Therefore, alternative b) 3(x + 6) is correct.

question 5

Knowing that the sum of three consecutive numbers equals 18, write the corresponding algebraic expression and calculate the first number in the sequence.

See Answer

Correct answer: x + (x+1) + (x+2) and x = 5.

Let's call the first number in the sequence x. If the numbers are consecutive, then the next number in the sequence has one more unit than the previous one.

1st number: x
2nd number: x + 1
3rd number: x + 2

Therefore, the algebraic expression that presents the sum of the three consecutive numbers is:

x + (x + 1) + (x + 2)

Knowing that the result of the sum is 18, we calculate the value of x as follows:

x + (x + 1) + (x + 2) = 18
x + x + x = 18 - 1 - 2
3x = 15
x = 15/3
x = 5

Therefore, the first number in the sequence is 5.

question 6

Carla thought of a number and added 4 units to it. After that, Carla multiplied the result by 2 and added her own number. Knowing that the result of the expressed was 20, which number did Carla choose?

a) 8
b) 6
c) 4
d) 2

See Answer

Correct alternative: c) 4.

Let's use the letter x to represent the number Carla thought.

First, Carla added 4 units to x, that is, x + 4.

By multiplying the result by 2, we have 2(x+4) and, finally, the thought number itself was added:

2(x+4) + x

If the result of the expression is 20, we can calculate the number that Carla chose as follows:

2(x + 4) + x = 20
2x + 8 + x = 20
3x = 20 - 8
3x = 12
x = 12/3
x = 4

Therefore, the number chosen by Carla was 4, as per alternative c).

question 7

Carlos has a small greenhouse in his backyard, where he grows some species of plants. As plants must be subjected to a certain temperature, Carlos regulates the temperature based on algebraic expression , as a function of time t.

When t = 12h, what is the temperature reached by the greenhouse?

a) 34°C
b) 24°C
c) 14°C
d) 44°C

See Answer

Correct alternative: b) 24°C.

To know the temperature reached by the stove, we must substitute the value of time (t) in the expression. When t=12h, we have:

Therefore, when t = 12h, the oven temperature is 24 ºC.

question 8

Paula set up her own business and decided to sell two types of cake to start with. A chocolate cake costs R$ 15.00 and a vanilla cake costs R$ 12.00. If x is the amount of chocolate cake sold and y is the amount of vanilla cake sold, how much will Paula earn selling 5 units and 7 units, respectively, of each type of cake?

a) BRL 210.00
b) BRL 159.00
c) BRL 127.00
d) BRL 204.00

See Answer

Correct alternative: b) R$ 159.00.

If each chocolate cake sells for R$15.00 and the amount sold is x, then Paula will earn 15.x for the chocolate cakes sold.

As the vanilla cake costs R$ 12.00 and are sold y cakes, so Paula will earn 12.y for the vanilla cakes.

Joining the two values ​​we have the algebraic expression for the presented problem: 15x + 12y.

Replacing the values ​​of x and y by the amounts presented, we can calculate the total collected by Paula:

15x + 12y =
= 15.5 + 12.7 =
= 75 + 84 =
= 159

Therefore, Paula will earn R$ 159.00, according to alternative b).

question 9

Write an algebraic expression to calculate the perimeter of the figure below and determine the result for x = 2 and y = 4.

See Answer

Correct answer: P = 4x + 6y and P = 32.

The perimeter of a rectangle is calculated using the formula:

P = 2b + 2h

Where,

P is the perimeter
b is the base
h is the height

So the perimeter of the rectangle is twice the base plus twice the height. Substituting b by 3y and h by 2x, we have the following algebraic expression:

P = 2.2x + 2.3y
P = 4x + 6y

Now, we apply the values ​​of x and y given in the statement to the expression.

P = 4.2 + 6.4
P = 8 + 24
P = 32

So the perimeter of the rectangle is 32.

question 10

Simplify the following algebraic expressions.

a) (2x² – 3x + 8) – (2x -2).(x+3)

See Answer

Correct answer: -7x + 14.

1st step: multiply term by term

Note that the (2x - 2).(x+3) part of the expression has a multiplication. Therefore, we started the simplification by solving the operation by multiplying term by term.

(2x - 2).(x+3) = 2x.x + 2x.3 - 2.x - 2.3 = 2x² + 6x – 2x – 6

Once this is done, the expression becomes (2x² – 3x + 8) – (2x² + 6x – 2x – 6)

2nd step: invert the signal

Note that the minus sign in front of the parentheses reverses all of the signs inside the parentheses, meaning that what is positive will become negative and what is negative will become positive.

– (2x² + 6x – 2x – 6) = – 2x² – 6x + 2x + 6

Now, the expression becomes (2x² – 3x + 8) – 2x² – 6x + 2x + 6.

3rd step: perform operations with similar terms

To make the calculations easier, let's rearrange the expression to keep similar terms together.

(2x² – 3x + 8) – 2x² – 6x + 2x + 6 = 2x² – 2x² – 3x – 6x + 2x + 8 + 6

Note that operations are addition and subtraction. To solve them we must add or subtract the coefficients and repeat the literal part.

2x² – 2x² – 3x – 6x + 2x + 8 + 6 = 0 – 9x + 2x + 14 = -7x + 14

Therefore, the simplest possible form of the algebraic expression (2x² – 3x + 8) – (2x-2). (x+3) is - 7x + 14.

b) (6x - 4x²) + (5 - 4x) - (7x² – 2x – 3) + (8 – 4x)

See Answer

Correct answer: – 11x² + 16.

1st step: remove the terms from the parentheses and change the sign

Remember that if the sign before the parentheses is negative, the terms inside the parentheses will have their signs reversed. What is negative becomes positive and what is positive becomes negative.

(6x - 4x²) + (5 - 4x) - (7x² – 2x – 3) + (8 – 4x) = 6x – 4x² + 5 - 4x - 7x² + 2x + 3 + 8 - 4x

2nd step: group similar terms

To make your calculations easier, view similar terms and place them close together. This will make it easier to identify the operations to carry out.

6x - 4x² + 5 - 4x - 7x² + 2x + 3 + 8 – 4x = – 4x² – 7x² + 6x – 4x + 2x – 4x + 5 + 3 + 8

3rd step: perform operations with similar terms

To simplify the expression we must add or subtract the coefficients and repeat the literal part.

– 4x² – 7x² + 6x – 4x + 2x – 4x + 5 + 3 + 8 = – 11x² + 0 + 16 = – 11x² + 16

Therefore, the simplest possible form of the expression (6x – 4x²) + (5 - 4x) - (7x² – 2x – 3) + (8 – 4x) is – 11x² + 16.

ç)

See Answer

Correct answer: 2b² - 3b.

Note that the literal part of the denominator is the²B. To simplify the expression we must highlight the literal part of the numerator that is equal to the denominator.

Therefore, 4th²B³ can be rewritten as the²b.4b² and 6th³B² becomes the²b.6ab.

We now have the following expression: .

The terms equal to²b are canceled because the²b/a²b = 1. We are left with the expression: .

Dividing coefficients 4 and 6 by the denominator 2, we obtain the simplified expression: 2b² - 3b.

To learn more, read:

• Algebraic Expressions
• Numerical Expressions
• Polynomials
• Notable products