Sure, let's solve the given equation step by step:
The equation given is:
[tex]\[ 2x - 3 = 3(5x - 12) \][/tex]
Step 1: Distribute the 3 on the right-hand side of the equation:
[tex]\[ 2x - 3 = 3 \cdot 5x - 3 \cdot 12 \][/tex]
[tex]\[ 2x - 3 = 15x - 36 \][/tex]
Step 2: To get all the terms involving [tex]\( x \)[/tex] on one side and constant terms on the other side, subtract [tex]\( 15x \)[/tex] from both sides:
[tex]\[ 2x - 15x - 3 = -36 \][/tex]
[tex]\[ -13x - 3 = -36 \][/tex]
Step 3: Add 3 to both sides to isolate the term involving [tex]\( x \)[/tex]:
[tex]\[ -13x - 3 + 3 = -36 + 3 \][/tex]
[tex]\[ -13x = -33 \][/tex]
Step 4: Divide both sides by -13 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{-33}{-13} \][/tex]
[tex]\[ x = \frac{33}{13} \][/tex]
So, the solution to the equation [tex]\( 2x - 3 = 3(5x - 12) \)[/tex] is:
[tex]\[ x = \frac{33}{13} \][/tex]
