Question
Remember that you can use inverse operations to solve equations. For \( 1-3 \), solve. 1. \( 4+2+h=10 \) 2. \( 4 x-3=17 \) 3. \( (v-8) \div 12=2 \)
Ask by Schultz Chang. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
1. \( h = 4 \)
2. \( x = 5 \)
3. \( v = 32 \)
Solution
**1. Equation:** \( 4+2+h=10 \)
- Simplify the left side: \( 4+2=6 \), so the equation becomes
\[
6+h=10.
\]
- Use the inverse operation of addition by subtracting \( 6 \) from both sides:
\[
h=10-6.
\]
- Simplify the result:
\[
h=4.
\]
---
**2. Equation:** \( 4x-3=17 \)
- Use the inverse operation of subtraction by adding \( 3 \) to both sides:
\[
4x=17+3.
\]
- Simplify the right side:
\[
4x=20.
\]
- Use the inverse operation of multiplication by dividing both sides by \( 4 \):
\[
x=\frac{20}{4}.
\]
- Simplify the fraction:
\[
x=5.
\]
---
**3. Equation:** \( (v-8) \div 12=2 \)
- Rewrite the division as:
\[
\frac{v-8}{12}=2.
\]
- Use the inverse operation of division by multiplying both sides by \( 12 \):
\[
v-8=2\times12.
\]
- Simplify the product:
\[
v-8=24.
\]
- Use the inverse operation of subtraction by adding \( 8 \) to both sides:
\[
v=24+8.
\]
- Simplify the result:
\[
v=32.
\]
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Simplify this solution The Deep Dive
To find the value of \( h \) in the equation \( 4 + 2 + h = 10 \), first combine the numbers on the left side to get \( 6 + h = 10 \). Now, use the inverse operation: subtract 6 from both sides to isolate \( h \). Thus, \( h = 10 - 6 \) which simplifies to \( h = 4 \). For the equation \( 4x - 3 = 17 \), start by adding 3 to both sides to get \( 4x = 20 \). Now, divide both sides by 4 to solve for \( x \), yielding \( x = 20 ÷ 4 \), which gives you \( x = 5 \). To solve \( (v - 8) \div 12 = 2 \), multiply both sides by 12 to eliminate the division, resulting in \( v - 8 = 24 \). Finally, add 8 to both sides to find \( v = 24 + 8 \), hence \( v = 32 \).
