Literal Equations Ws | Download Free PDF | Area | Elementary ... - Free Printable

Absolutely! Let’s solve each problem step by step — both the Regular Equations (left column) and the Literal Equations (right column). Literal equations involve solving for one variable in terms of other variables, rather than finding a numerical value.

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## 🔢 Regular Equations

1a) \( x - 7 = 8 \)

Goal: Solve for \( x \)

Step 1: Add 7 to both sides to isolate \( x \)

\[
x - 7 + 7 = 8 + 7
\]

\[
x = 15
\]

✔ Answer: \( x = 15 \)

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2a) \( 4x = -12 \)

Goal: Solve for \( x \)

Step 1: Divide both sides by 4

\[
\frac{4x}{4} = \frac{-12}{4}
\]

\[
x = -3
\]

✔ Answer: \( x = -3 \)

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3a) \( 2x - 5 = 11 \)

Goal: Solve for \( x \)

Step 1: Add 5 to both sides

\[
2x - 5 + 5 = 11 + 5
\]

\[
2x = 16
\]

Step 2: Divide both sides by 2

\[
\frac{2x}{2} = \frac{16}{2}
\]

\[
x = 8
\]

✔ Answer: \( x = 8 \)

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4a) \( \frac{1}{2}(4x) = -20 \)

Goal: Solve for \( x \)

Step 1: Simplify left side: \( \frac{1}{2} \cdot 4x = 2x \)

\[
2x = -20
\]

Step 2: Divide both sides by 2

\[
x = \frac{-20}{2} = -10
\]

✔ Answer: \( x = -10 \)

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5a) \( \frac{x}{-8} = 11 \)

Goal: Solve for \( x \)

Step 1: Multiply both sides by -8

\[
x = 11 \cdot (-8)
\]

\[
x = -88
\]

✔ Answer: \( x = -88 \)

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## 📐 Literal Equations (Solve for specified variable)

1b) Solve for \( x \): \( x - b = a \)

Goal: Isolate \( x \)

Step 1: Add \( b \) to both sides

\[
x - b + b = a + b
\]

\[
x = a + b
\]

✔ Answer: \( x = a + b \)

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2b) Solve for \( k \): \( -3k = m \)

Goal: Isolate \( k \)

Step 1: Divide both sides by -3

\[
k = \frac{m}{-3} = -\frac{m}{3}
\]

✔ Answer: \( k = -\frac{m}{3} \)

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3b) Solve for \( b \): \( 2b - 9 = d \)

Goal: Isolate \( b \)

Step 1: Add 9 to both sides

\[
2b = d + 9
\]

Step 2: Divide both sides by 2

\[
b = \frac{d + 9}{2}
\]

✔ Answer: \( b = \frac{d + 9}{2} \)

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4b) Solve for \( g \): \( aeg = 10 \)

Goal: Isolate \( g \)

Step 1: Divide both sides by \( ae \) (assuming \( a \neq 0 \), \( e \neq 0 \))

\[
g = \frac{10}{ae}
\]

✔ Answer: \( g = \frac{10}{ae} \)

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5b) Solve for \( y \): \( \frac{y}{3} = h \)

Goal: Isolate \( y \)

Step 1: Multiply both sides by 3

\[
y = 3h
\]

✔ Answer: \( y = 3h \)

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## ✔ Final Answers Summary:

Regular Equations:

1a) \( x = 15 \)
2a) \( x = -3 \)
3a) \( x = 8 \)
4a) \( x = -10 \)
5a) \( x = -88 \)

Literal Equations:

1b) \( x = a + b \)
2b) \( k = -\frac{m}{3} \)
3b) \( b = \frac{d + 9}{2} \)
4b) \( g = \frac{10}{ae} \)
5b) \( y = 3h \)

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Let me know if you’d like these explained with diagrams or further examples! 😊