Correct answers:
a) x = 9
b) x = 4
c) x = 6
d) x = 5
To solve an equation of the first degree we must isolate the unknown on one side of the equality and the constant values on the other. Remember that when changing a term in the equation to the other side of the equals sign, we must reverse the operation. For example, what was adding starts to subtract and vice versa.
a) Correct answer: x = 9.
b) Correct answer: x = 4
c) Correct answer: x = 6
d) Correct answer: x = 5
Correct answer: x = - 6/11.
First, we must eliminate the parentheses. For this, we apply the distributive property of multiplication.
Now we can find the unknown value by isolating the x on one side of the equality.
Correct answer: 11/3.
Note that the equation has fractions. To solve it we first need to reduce the fractions to the same denominator. Therefore, we must calculate the least common multiple between them.
Now we divide the MMC 12 by the denominator of each fraction and the result must be multiplied by the numerator. This value becomes the numerator, while the denominator of all terms is 12.
After canceling the denominators, we can isolate the unknown and calculate the value of x.
Correct answer: - 1/3.
1st step: calculate the MMC of the denominators.
2nd step: divide the MMC by the denominator of each fraction and multiply the result by the numerator. After that, we replace the numerator with the result calculated previously and the denominator with the MMC.
3rd step: cancel the denominator, isolate the unknown and calculate its value.
The minus sign before the parentheses changes the signs of the terms inside.
-1. 5x = -5x
-1. (-7) = 7
Continuing the equation:
Correct answers:
a) y = 2
b) x = 6
c) y.x = 12
d) y/x = 1/3
a) y = 2
b) x = 6
c) y.x = 12
y. x = 2. 6 = 12
d) y/x = 1/3
Correct answer: b) 38.
To build an equation there must be two members: one before and one after the equals sign. Each component of the equation is called a term.
The terms in the first member of the equation are double the unknown number and 6 units. The values must be added, therefore: 2x + 6.
The second member of the equation contains the result of this operation, which is 82. Assembling the equation of the first degree with an unknown, we have:
2x + 6 = 82
Now, we solve the equation by isolating the unknown in one member and transferring the number 6 to the second member. To do this, the number 6, which was positive, becomes negative.
2x + 6 = 82
2x = 82 - 6
2x = 76
x = 38
So the unknown number is 38.
Correct answer: d) 20.
The perimeter of a rectangle is the sum of its sides. The long side is called the base and the short side is called the height.
According to the statement data, if the short side of the rectangle is x, then the long side is (x + 10).
A rectangle is a quadrilateral, so its perimeter is the sum of the two longest sides and the two shortest sides. This can be expressed in equation form as follows:
2x + 2(x+10) = 100
To find the measure of the short side, just solve the equation.
2x + 2(x+10) = 100
2x + 2x + 20 = 100
4x = 100 - 20
4x = 80
x = 80/4
x = 20
Correct alternative: c) 40.
We can use the unknown x to represent the original length of the piece. Thus, after being washed, the piece lost 1/10 of its x length.
The first way you can resolve this issue is:
x - 0.1x = 36
0.9x = 36
x = 36/0.9
x = 40
The second form, on the other hand, needs the mmc of the denominators, which is 10.
Now we calculate the new numerators by dividing the mmc by the initial denominator and multiplying the result by the initial numerator. After that, we cancel the denominator 10 of all terms and solve the equation.
Therefore, the original length of the piece was 40 m.
Correct alternative: c) 2310 m.
Since the total path is the unknown value, let's call it x.
The terms of the first member of the equation are:
- Race: 2/7x
- Walk: 5/11x
- additional stretch: 600
The sums of all these values result in the length of the run, which we call x. Therefore, the equation can be written as:
2/7x + 5/11x + 600 = x
To solve this equation of the first degree we need to calculate the mmc of the denominators.
mmc (7.11) = 77
Now we replace the terms in the equation.
Therefore, the total length of the path is 2310 m.
Correct alternative: c) 300.
If B's number of hits was x, then A's number of hits was x + 40%. This percentage can be written as the fraction 40/100 or as the decimal number 0.40.
Therefore, the equation that determines the number of correct answers can be:
x + x + 40/100x = 720 or x + x + 0.40x = 720
Resolution 1:
Resolution 2:
Therefore, B's number of hits was 300.
Correct answer: 9, 10, 11, 12, 13, 14 and 15.
By assigning the unknown x to the first number in the sequence, then the number's successor is x+1, and so on.
The first member of the equation is formed by the sum of the first four numbers in the sequence and the second member, after equality, presents the last three. So we can write the equation like this:
x + (x+1) + (x+2) + (x+3) = (x+4) + (x+5) + (x+6)
4x + 6 = 3x + 15
4x - 3x = 15 - 6
x = 9
Thus, the first term is 9 and the sequence is formed by the seven numbers: 9, 10, 11, 12, 13, 14 and 15.
