Let's solve each of the equations step by step, ensuring to show all the work for full credit.
Question 1
Equation:
\( 4x + 7 = 23 - 8 \)
Step 1: Simplify the right side of the equation.
\( 23 - 8 = 15 \)
So, the equation becomes:
\( 4x + 7 = 15 \)
Step 2: Subtract 7 from both sides.
\[
4x + 7 - 7 = 15 - 7 \
4x = 8
\]
Step 3: Divide both sides by 4.
\[
\frac{4x}{4} = \frac{8}{4} \
x = 2
\]
Final answer:
\( x = 2 \)
Question 2
Equation:
\( -5 = 3m - 14 + 12 \)
Step 1: Simplify the right side of the equation.
\[
-14 + 12 = -2 \
-5 = 3m - 2
\]
Step 2: Add 2 to both sides.
\[
-5 + 2 = 3m - 2 + 2 \
-3 = 3m
\]
Step 3: Divide both sides by 3.
\[
\frac{-3}{3} = \frac{3m}{3} \
m = -1
\]
Final answer:
\( m = -1 \)
Question 3
Equation:
\( 7(x - 9) = -21 + 21 \)
Step 1: Simplify the right side of the equation.
\[
-21 + 21 = 0 \
7(x - 9) = 0
\]
Step 2: Divide both sides by 7.
\[
\frac{7(x-9)}{7} = \frac{0}{7} \
x - 9 = 0
\]
Step 3: Add 9 to both sides.
\[
x = 9
\]
Final answer:
\( x = 9 \)
Question 4
Equation:
\( 7x - 5 = 3x + 15 \)
Step 1: Subtract \( 3x \) from both sides.
\[
7x - 3x - 5 = 15 \
4x - 5 = 15
\]
Step 2: Add 5 to both sides.
\[
4x - 5 + 5 = 15 + 5 \
4x = 20
\]
Step 3: Divide both sides by 4.
\[
\frac{4x}{4} = \frac{20}{4} \
x = 5
\]
Final answer:
\( x = 5 \)
Question 5
Equation:
\( 8x - 8 = -4x + 16 - 100 \)
Step 1: Simplify the right side of the equation.
\[
16 - 100 = -84 \
8x - 8 = -4x - 84
\]
Step 2: Add \( 4x \) to both sides.
\[
8x + 4x - 8 = -84 \
12x - 8 = -84
\]
Step 3: Add 8 to both sides.
\[
12x - 8 + 8 = -84 + 8 \
12x = -76
\]
Step 4: Divide both sides by 12.
\[
x = \frac{-76}{12} \
x = -\frac{19}{3} = -6.33 \text{ (approximately)}
\]
Final answer:
\( x = -\frac{19}{3} \) or \( -6.33 \) (rounded)
Feel free to ask if you need further clarification or additional problems to solve!
1 answer