Question

1. solving equations 7.ee.b.4

2a - 5 = 3
2.

• 14x + 3 = - 25

3.
4y - 7 = 9
4.
5 + 10x = 25
5.

• x + 3 = 6

6.
4x - 3 = 13
7.
(1/4)x + 2 = 3
8.
12 + 5x - 2x = 27
9.

• x + 2x + 4x = 35

10.
0.5x + (- 1.5x) - 0.4 = - 2.4

Explanation:

Problem 1:

Step1: Add 5 to both sides

$2a - 5 + 5 = 3 + 5$
$2a = 8$

Step2: Divide by 2 on both sides

$a = \frac{8}{2}$

Problem 2:

Step1: Subtract 3 from both sides

$-14x + 3 - 3 = -25 - 3$
$-14x = -28$

Step2: Divide by -14 on both sides

$x = \frac{-28}{-14}$

Problem 3:

Step1: Add 7 to both sides

$4y - 7 + 7 = 9 + 7$
$4y = 16$

Step2: Divide by 4 on both sides

$y = \frac{16}{4}$

Problem 4:

Step1: Subtract 5 from both sides

$5 + 10x - 5 = 25 - 5$
$10x = 20$

Step2: Divide by 10 on both sides

$x = \frac{20}{10}$

Problem 5:

Step1: Subtract 3 from both sides

$-x + 3 - 3 = 6 - 3$
$-x = 3$

Step2: Multiply by -1 on both sides

$x = -3$

Problem 6:

Step1: Add 3 to both sides

$4x - 3 + 3 = 13 + 3$
$4x = 16$

Step2: Divide by 4 on both sides

$x = \frac{16}{4}$

Problem 7:

Step1: Subtract 2 from both sides

$\frac{1}{4}x + 2 - 2 = 3 - 2$
$\frac{1}{4}x = 1$

Step2: Multiply by 4 on both sides

$x = 1 \times 4$

Problem 8:

Step1: Combine like terms

$12 + (5x - 2x) = 27$
$12 + 3x = 27$

Step2: Subtract 12 from both sides

$3x = 27 - 12$
$3x = 15$

Step3: Divide by 3 on both sides

$x = \frac{15}{3}$

Problem 9:

Step1: Combine like terms

$(-x + 2x + 4x) = 35$
$5x = 35$

Step2: Divide by 5 on both sides

$x = \frac{35}{5}$

Problem 10:

Step1: Combine like terms

$(0.5x - 1.5x) - 0.4 = -2.4$
$-x - 0.4 = -2.4$

Step2: Add 0.4 to both sides

$-x = -2.4 + 0.4$
$-x = -2$

Step3: Multiply by -1 on both sides

$x = 2$

Answer:

1. $a = 4$
2. $x = 2$
3. $y = 4$
4. $x = 2$
5. $x = -3$
6. $x = 4$
7. $x = 4$
8. $x = 5$
9. $x = 7$
10. $x = 2$