Let's solve each of the linear equations step by step.
---
Problem 15: \( 5 - 2(x + 9) = 25 \)
1.
Expand the parentheses:
\[
5 - 2(x + 9) = 25
\]
\[
5 - 2x - 18 = 25
\]
2.
Combine like terms:
\[
5 - 18 - 2x = 25
\]
\[
-13 - 2x = 25
\]
3.
Isolate the term with \( x \):
\[
-2x = 25 + 13
\]
\[
-2x = 38
\]
4.
Solve for \( x \):
\[
x = \frac{38}{-2}
\]
\[
x = -19
\]
Solution to Problem 15:
\[
\boxed{-19}
\]
---
Problem 16: \( 5(x + 2) = 3(x - 4) \)
1.
Expand both sides:
\[
5(x + 2) = 3(x - 4)
\]
\[
5x + 10 = 3x - 12
\]
2.
Move all \( x \)-terms to one side and constants to the other:
\[
5x - 3x = -12 - 10
\]
\[
2x = -22
\]
3.
Solve for \( x \):
\[
x = \frac{-22}{2}
\]
\[
x = -11
\]
Solution to Problem 16:
\[
\boxed{-11}
\]
---
Problem 17: \( 3(2x - 4) = 12 \)
1.
Expand the parentheses:
\[
3(2x - 4) = 12
\]
\[
6x - 12 = 12
\]
2.
Isolate the term with \( x \):
\[
6x = 12 + 12
\]
\[
6x = 24
\]
3.
Solve for \( x \):
\[
x = \frac{24}{6}
\]
\[
x = 4
\]
Solution to Problem 17:
\[
\boxed{4}
\]
---
Problem 18: \( \frac{2}{3}x + 5 = \frac{1}{4}x \)
1.
Eliminate the fractions by finding a common denominator (LCM of 3 and 4 is 12):
Multiply every term by 12:
\[
12 \left( \frac{2}{3}x \right) + 12(5) = 12 \left( \frac{1}{4}x \right)
\]
\[
8x + 60 = 3x
\]
2.
Move all \( x \)-terms to one side:
\[
8x - 3x = -60
\]
\[
5x = -60
\]
3.
Solve for \( x \):
\[
x = \frac{-60}{5}
\]
\[
x = -12
\]
Solution to Problem 18:
\[
\boxed{-12}
\]
---
Problem 19: \( \frac{4x}{5} + x = \frac{1}{2}x \)
1.
Eliminate the fractions by finding a common denominator (LCM of 5 and 2 is 10):
Multiply every term by 10:
\[
10 \left( \frac{4x}{5} \right) + 10(x) = 10 \left( \frac{1}{2}x \right)
\]
\[
8x + 10x = 5x
\]
2.
Combine like terms:
\[
18x = 5x
\]
3.
Isolate \( x \):
\[
18x - 5x = 0
\]
\[
13x = 0
\]
4.
Solve for \( x \):
\[
x = 0
\]
Solution to Problem 19:
\[
\boxed{0}
\]
---
Problem 20: \( \frac{5x + 3}{6} = 3 \)
1.
Eliminate the fraction by multiplying both sides by 6:
\[
6 \left( \frac{5x + 3}{6} \right) = 6(3)
\]
\[
5x + 3 = 18
\]
2.
Isolate the term with \( x \):
\[
5x = 18 - 3
\]
\[
5x = 15
\]
3.
Solve for \( x \):
\[
x = \frac{15}{5}
\]
\[
x = 3
\]
Solution to Problem 20:
\[
\boxed{3}
\]
---
Final Answers:
\[
\boxed{-19, -11, 4, -12, 0, 3}
\]
Parent Tip: Review the logic above to help your child master the concept of solutions to linear equations worksheet.
