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Inverse Operations:

Solve each equation for the variable. Show your work.

1) [tex]\( x + 5 = 20 \)[/tex]
2) [tex]\( 15.45 = b + 3.1 \)[/tex]
3) [tex]\( a - 8 = -11 \)[/tex]

Sagot :

GinnyAnswer
Sure, let's solve these equations step-by-step using inverse operations.

### 1) [tex]\( x + 5 = 20 \)[/tex]

To solve for [tex]\( x \)[/tex], we need to isolate [tex]\( x \)[/tex] on one side of the equation. We can do this by performing the inverse operation of addition, which is subtraction.

Subtract 5 from both sides of the equation:
[tex]\[ x + 5 - 5 = 20 - 5 \][/tex]

Simplify both sides:
[tex]\[ x = 15 \][/tex]

So, [tex]\( x = 15 \)[/tex].

### 2) [tex]\( 15.45 = b + 3.1 \)[/tex]

To solve for [tex]\( b \)[/tex], we again need to isolate [tex]\( b \)[/tex] on one side of the equation. This time, we perform the inverse operation of addition, which is subtraction.

Subtract 3.1 from both sides of the equation:
[tex]\[ 15.45 - 3.1 = b + 3.1 - 3.1 \][/tex]

Simplify both sides:
[tex]\[ 12.35 = b \][/tex]

So, [tex]\( b = 12.35 \)[/tex].

### 3) [tex]\( a - 8 = -11 \)[/tex]

To solve for [tex]\( a \)[/tex], we need to isolate [tex]\( a \)[/tex] on one side of the equation. This time, we perform the inverse operation of subtraction, which is addition.

Add 8 to both sides of the equation:
[tex]\[ a - 8 + 8 = -11 + 8 \][/tex]

Simplify both sides:
[tex]\[ a = -3 \][/tex]

So, [tex]\( a = -3 \)[/tex].

In summary:
1. [tex]\( x = 15 \)[/tex]
2. [tex]\( b = 12.35 \)[/tex]
3. [tex]\( a = -3 \)[/tex]
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