Question

3(4x - 5) + 2(11 - 2x) = 43 check:

Explanation:

Step1: Expand the expressions

$3(4x - 5)+2(11 - 2x)=12x-15 + 22-4x$

Step2: Combine like - terms

$12x-4x-15 + 22=(12x-4x)+(-15 + 22)=8x + 7$

Step3: Solve the equation

We have the equation $8x+7 = 43$. Subtract 7 from both sides: $8x+7-7=43 - 7$, which gives $8x=36$. Then divide both sides by 8: $x=\frac{36}{8}=\frac{9}{2}=4.5$

Step4: Check the solution

Substitute $x = 4.5$ into the original equation:
Left - hand side: $3(4\times4.5-5)+2(11-2\times4.5)=3(18 - 5)+2(11 - 9)=3\times13+2\times2=39 + 4=43$
Right - hand side: 43
Since the left - hand side equals the right - hand side when $x = 4.5$, the solution is correct.

Answer:

$x = 4.5$