Question

solve each equation.
1 2x + 5 = 17
2 3y - 4 = 11
3 5a + 10 = 35
4 4b - 6 = 14
5 2(m - 3) = 10

Explanation:

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

Step 1: Subtract 5 from both sides

To isolate the term with \( x \), we subtract 5 from both sides of the equation.
\( 2x + 5 - 5 = 17 - 5 \)
\( 2x = 12 \)

Step 2: Divide both sides by 2

To solve for \( x \), we divide both sides of the equation by 2.
\( \frac{2x}{2} = \frac{12}{2} \)
\( x = 6 \)

Step 1: Add 4 to both sides

To isolate the term with \( y \), we add 4 to both sides of the equation.
\( 3y - 4 + 4 = 11 + 4 \)
\( 3y = 15 \)

Step 2: Divide both sides by 3

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

Step 1: Subtract 10 from both sides

To isolate the term with \( a \), we subtract 10 from both sides of the equation.
\( 5a + 10 - 10 = 35 - 10 \)
\( 5a = 25 \)

Step 2: Divide both sides by 5

To solve for \( a \), we divide both sides of the equation by 5.
\( \frac{5a}{5} = \frac{25}{5} \)
\( a = 5 \)

Answer:

\( x = 6 \)

Problem 2: Solve \( 3y - 4 = 11 \)