Question

lesson 6-2 reteach
using addition to undo subtraction
addition \undoes\ subtraction. adding the same number to both sides of an equation keeps the equation balanced.
$x - 5 = -6.3$
$x - 5 + 5 = -6.3 + 5$
$x = -1.3$
using subtraction to undo addition
subtraction \undoes\ addition. subtracting a number from both sides of an equation keeps the equation balanced.
$n + \frac{3}{4} = -15$
$n + \frac{3}{4} - \frac{3}{4} = -15 - \frac{3}{4}$
$n = -15\frac{3}{4}$
be careful to identify the correct number that is to be added or subtracted from both sides of an equation. the numbers and variables can move around, as the problems show.
solve using addition or subtraction.

1. $6 = m - \frac{7}{8}$
2. $3.9 + t = 4.5$
3. $10 = -3.1 + j$

Explanation:

Problem 1: Solve \( 6 = m - \frac{7}{8} \)

Step 1: Add \( \frac{7}{8} \) to both sides

To isolate \( m \), we use the property that addition undoes subtraction. Add \( \frac{7}{8} \) to both sides of the equation:
\( 6 + \frac{7}{8} = m - \frac{7}{8} + \frac{7}{8} \)

Step 2: Simplify both sides

Simplify the left side: \( 6 + \frac{7}{8} = \frac{48}{8} + \frac{7}{8} = \frac{55}{8} = 6\frac{7}{8} \)
The right side simplifies to \( m \) (since \( -\frac{7}{8} + \frac{7}{8} = 0 \)). So \( m = 6\frac{7}{8} \) (or \( \frac{55}{8} \)).

Problem 2: Solve \( 3.9 + t = 4.5 \)

Step 1: Subtract \( 3.9 \) from both sides

To isolate \( t \), use subtraction (since subtraction undoes addition). Subtract \( 3.9 \) from both sides:
\( 3.9 + t - 3.9 = 4.5 - 3.9 \)

Step 2: Simplify both sides

Simplify the left side: \( t \) (since \( 3.9 - 3.9 = 0 \)).
Simplify the right side: \( 4.5 - 3.9 = 0.6 \). So \( t = 0.6 \).

Problem 3: Solve \( 10 = -3.1 + j \)

Step 1: Add \( 3.1 \) to both sides

To isolate \( j \), use addition (since addition undoes subtraction). Add \( 3.1 \) to both sides:
\( 10 + 3.1 = -3.1 + j + 3.1 \)

Step 2: Simplify both sides

Simplify the left side: \( 13.1 \).
Simplify the right side: \( j \) (since \( -3.1 + 3.1 = 0 \)). So \( j = 13.1 \).

Answer:

s:

1. \( \boldsymbol{m = 6\frac{7}{8}} \) (or \( \boldsymbol{\frac{55}{8}} \))
2. \( \boldsymbol{t = 0.6} \)
3. \( \boldsymbol{j = 13.1} \)