Answered

Solve for [tex]\( x \)[/tex].

[tex]\[ 2(3x - 2.7) = 3x - 5.4 \][/tex]

[tex]\[ x = \square \][/tex] (Type an integer or a decimal.)



Answer :

Certainly! Let's solve the equation step by step.

1. Start with the given equation:
[tex]\[ 2(3x - 2.7) = 3x - 5.4 \][/tex]

2. Distribute the 2 on the left-hand side:
[tex]\[ 2 \cdot (3x) - 2 \cdot 2.7 = 3x - 5.4 \][/tex]
Simplifying the multiplications:
[tex]\[ 6x - 5.4 = 3x - 5.4 \][/tex]

3. Now, we have:
[tex]\[ 6x - 5.4 = 3x - 5.4 \][/tex]

4. To isolate the [tex]\( x \)[/tex] terms, subtract [tex]\( 3x \)[/tex] from both sides of the equation:
[tex]\[ 6x - 3x - 5.4 = 3x - 3x - 5.4 \][/tex]
Simplifying this:
[tex]\[ 3x - 5.4 = -5.4 \][/tex]

5. Next, add 5.4 to both sides to isolate the [tex]\( x \)[/tex] term:
[tex]\[ 3x - 5.4 + 5.4 = -5.4 + 5.4 \][/tex]
Simplifying this:
[tex]\[ 3x = 0 \][/tex]

6. Finally, divide both sides by 3 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{0}{3} \][/tex]
Simplifying:
[tex]\[ x = 0 \][/tex]

Therefore, the solution to the equation [tex]\( 2(3x - 2.7) = 3x - 5.4 \)[/tex] is:
[tex]\[ x = 0 \][/tex]