Question
Angles FEG and DEG are complementary angles. The equation to solve for x is : ( 5x - 22) + ( 2x ) = 90. Fill in the blanks with correct steps for solving x
Answers
GPT-4o mini
To solve the equation \( (5x - 22) + (2x) = 90 \) for \( x \), follow these steps:
1. **Combine like terms.** The equation is:
\[
5x - 22 + 2x = 90
\]
Combine \( 5x \) and \( 2x \):
\[
(5x + 2x) - 22 = 90
\]
\[
7x - 22 = 90
\]
2. **Add 22 to both sides.** This isolates the term with \( x \):
\[
7x - 22 + 22 = 90 + 22
\]
\[
7x = 112
\]
3. **Divide both sides by 7.** This solves for \( x \):
\[
x = \frac{112}{7}
\]
\[
x = 16
\]
So, the solution for \( x \) is \( 16 \).
1. **Combine like terms.** The equation is:
\[
5x - 22 + 2x = 90
\]
Combine \( 5x \) and \( 2x \):
\[
(5x + 2x) - 22 = 90
\]
\[
7x - 22 = 90
\]
2. **Add 22 to both sides.** This isolates the term with \( x \):
\[
7x - 22 + 22 = 90 + 22
\]
\[
7x = 112
\]
3. **Divide both sides by 7.** This solves for \( x \):
\[
x = \frac{112}{7}
\]
\[
x = 16
\]
So, the solution for \( x \) is \( 16 \).