Question

1. solve the equation, then verify & graph the solution.

-30 = -13x - 4

1. solve the equation, then verify & graph the solution.

22 - 3x = 40

solve the equation, then verify & graph the solution.
5x - 17 = -62

Explanation:

Problem 2: $-30 = -13x - 4$

Step1: Add 4 to both sides

$-30 + 4 = -13x - 4 + 4$
$-26 = -13x$

Step2: Divide by -13

$\frac{-26}{-13} = \frac{-13x}{-13}$
$2 = x$

Step3: Verify solution

Substitute $x=2$ into original equation:
$-30 = -13(2) - 4$
$-30 = -26 - 4$
$-30 = -30$ (True)

Step4: Graph explanation

Mark a closed dot at $2$ on a number line, as it is a single solution.

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Problem 4: $22 - 3x = 40$

Step1: Subtract 22 from both sides

$22 - 3x - 22 = 40 - 22$
$-3x = 18$

Step2: Divide by -3

$\frac{-3x}{-3} = \frac{18}{-3}$
$x = -6$

Step3: Verify solution

Substitute $x=-6$ into original equation:
$22 - 3(-6) = 40$
$22 + 18 = 40$
$40 = 40$ (True)

Step4: Graph explanation

Mark a closed dot at $-6$ on a number line, as it is a single solution.

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Problem 5: $5x - 17 = -62$

Step1: Add 17 to both sides

$5x - 17 + 17 = -62 + 17$
$5x = -45$

Step2: Divide by 5

$\frac{5x}{5} = \frac{-45}{5}$
$x = -9$

Step3: Verify solution

Substitute $x=-9$ into original equation:
$5(-9) - 17 = -62$
$-45 - 17 = -62$
$-62 = -62$ (True)

Step4: Graph explanation

Mark a closed dot at $-9$ on a number line, as it is a single solution.

Answer:

1. For $-30 = -13x - 4$:

Solution: $x=2$
Graph: Closed dot at 2 on a number line

1. For $22 - 3x = 40$:

Solution: $x=-6$
Graph: Closed dot at -6 on a number line

1. For $5x - 17 = -62$:

Solution: $x=-9$
Graph: Closed dot at -9 on a number line