Question

solve each equation. check your solution. (examples 1–4)

1. $5x + 2 = 17$
2. $19 = 4x + 3$
3. $-18 = 6 + 6x$
4. $-3x - 9 = -15$
5. $-6x - 7 = 17$
6. $-5 = 3x - 14$

Explanation:

Problem 1: \( 5x + 2 = 17 \)

Step 1: Subtract 2 from both sides

To isolate the term with \( x \), we subtract 2 from both sides of the equation.
\( 5x + 2 - 2 = 17 - 2 \)
\( 5x = 15 \)

Step 2: Divide both sides by 5

To solve for \( x \), we divide both sides of the equation by 5.
\( \frac{5x}{5} = \frac{15}{5} \)
\( x = 3 \)

Step 3: Check the solution

Substitute \( x = 3 \) back into the original equation:
Left side: \( 5(3) + 2 = 15 + 2 = 17 \)
Right side: \( 17 \)
Since both sides are equal, \( x = 3 \) is correct.

Step 1: Subtract 3 from both sides

To isolate the term with \( x \), we subtract 3 from both sides of the equation.
\( 19 - 3 = 4x + 3 - 3 \)
\( 16 = 4x \)

Step 2: Divide both sides by 4

To solve for \( x \), we divide both sides of the equation by 4.
\( \frac{16}{4} = \frac{4x}{4} \)
\( 4 = x \) or \( x = 4 \)

Step 3: Check the solution

Substitute \( x = 4 \) back into the original equation:
Left side: \( 19 \)
Right side: \( 4(4) + 3 = 16 + 3 = 19 \)
Since both sides are equal, \( x = 4 \) is correct.

Step 1: Subtract 6 from both sides

To isolate the term with \( x \), we subtract 6 from both sides of the equation.
\( -18 - 6 = 6 + 6x - 6 \)
\( -24 = 6x \)

Step 2: Divide both sides by 6

To solve for \( x \), we divide both sides of the equation by 6.
\( \frac{-24}{6} = \frac{6x}{6} \)
\( -4 = x \) or \( x = -4 \)

Step 3: Check the solution

Substitute \( x = -4 \) back into the original equation:
Left side: \( -18 \)
Right side: \( 6 + 6(-4) = 6 - 24 = -18 \)
Since both sides are equal, \( x = -4 \) is correct.

Answer:

\( x = 3 \)

Problem 2: \( 19 = 4x + 3 \)