Question

1. $-18 + \frac{x}{2} = -35$
2. $11 + 20x = -569$
3. $-15x - 2 = -482$
4. $\frac{3 + x}{-7} = 0$
5. $7 - 7x = 189$
6. $-90 = -3(20 + x)$
7. $\frac{3}{4}x + 7 = 22$
8. $-5(7 + x) = 20$
9. $\frac{1}{2}x - 5 = -13$

10)
11)
12)
13)
14)
15)
16)
17)
18)

Explanation:

Step1: Isolate the fractional term

Add 18 to both sides.
$$-18 + \frac{x}{2} + 18 = -35 + 18$$
$$\frac{x}{2} = -17$$

Step2: Solve for x

Multiply both sides by 2.
$$x = -17 \times 2$$
$$x = -34$$

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Step1: Isolate the variable term

Subtract 11 from both sides.
$$11 + 20x - 11 = -569 - 11$$
$$20x = -580$$

Step2: Solve for x

Divide both sides by 20.
$$x = \frac{-580}{20}$$
$$x = -29$$

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Step1: Isolate the variable term

Add 2 to both sides.
$$-15x - 2 + 2 = -482 + 2$$
$$-15x = -480$$

Step2: Solve for x

Divide both sides by -15.
$$x = \frac{-480}{-15}$$
$$x = 32$$

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Step1: Eliminate the denominator

Multiply both sides by -7.
$$\frac{3+x}{-7} \times (-7) = 0 \times (-7)$$
$$3 + x = 0$$

Step2: Solve for x

Subtract 3 from both sides.
$$x = 0 - 3$$
$$x = -3$$

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Step1: Isolate the variable term

Subtract 7 from both sides.
$$7 - 7x - 7 = 189 - 7$$
$$-7x = 182$$

Step2: Solve for x

Divide both sides by -7.
$$x = \frac{182}{-7}$$
$$x = -26$$

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Step1: Distribute the right-hand side

Expand the parentheses.
$$-90 = -60 - 3x$$

Step2: Isolate the variable term

Add 60 to both sides.
$$-90 + 60 = -3x$$
$$-30 = -3x$$

Step3: Solve for x

Divide both sides by -3.
$$x = \frac{-30}{-3}$$
$$x = 10$$

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Step1: Isolate the fractional term

Subtract 7 from both sides.
$$\frac{3}{4}x + 7 - 7 = 22 - 7$$
$$\frac{3}{4}x = 15$$

Step2: Solve for x

Multiply both sides by $\frac{4}{3}$.
$$x = 15 \times \frac{4}{3}$$
$$x = 20$$

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Step1: Divide to eliminate coefficient

Divide both sides by -5.
$$\frac{-5(7+x)}{-5} = \frac{20}{-5}$$
$$7 + x = -4$$

Step2: Solve for x

Subtract 7 from both sides.
$$x = -4 - 7$$
$$x = -11$$

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Step1: Isolate the fractional term

Add 5 to both sides.
$$\frac{1}{2}x - 5 + 5 = -13 + 5$$
$$\frac{1}{2}x = -8$$

Step2: Solve for x

Multiply both sides by 2.
$$x = -8 \times 2$$
$$x = -16$$

Answer:

1. $x = -34$
2. $x = -29$
3. $x = 32$
4. $x = -3$
5. $x = -26$
6. $x = 10$
7. $x = 20$
8. $x = -11$
9. $x = -16$