Questions: The goal of this problem is to solve the following equation: 12 x-(5 x-7)=49 First, simplify the equation by finding an equivalent left-hand side that does not contain parentheses: Simplified equation:

The goal of this problem is to solve the following equation:
12 x-(5 x-7)=49

First, simplify the equation by finding an equivalent left-hand side that does not contain parentheses:
Simplified equation:

Transcript text: The goal of this problem is to solve the following equation: \[ 12 x-(5 x-7)=49 \] First, simplify the equation by finding an equivalent left-hand side that does not contain parentheses: Simplified equation: $\square$

Solution

Solution Steps

To solve the equation $ 12x - (5x - 7) = 49 $, we need to first simplify the left-hand side by distributing and combining like terms. Then, we can isolate $ x $ by performing algebraic operations.

Distribute the negative sign inside the parentheses.
Combine like terms on the left-hand side.
Isolate $ x $ by moving constants to the right-hand side and dividing by the coefficient of $ x $.

Step 1: Distribute the Negative Sign

First, distribute the negative sign inside the parentheses: \[ 12x - (5x - 7) = 49 \implies 12x - 5x + 7 = 49 \]

Step 2: Combine Like Terms

Combine the like terms on the left-hand side: \[ (12x - 5x) + 7 = 49 \implies 7x + 7 = 49 \]

Step 3: Isolate $ x $

Subtract 7 from both sides to isolate the term with $ x $: \[ 7x + 7 - 7 = 49 - 7 \implies 7x = 42 \]

Step 4: Solve for $ x $

Divide both sides by 7 to solve for $ x $: \[ x = \frac{42}{7} \implies x = 6 \]