Question

Solve the equation: $6\left( 1-4x \right)+7\left( 2+5x \right)=53$

Answer 1

Hint: To simplify the equation given in the question, first open the brackets by using the distributive nature of multiplication over addition and subtraction, i.e., a(b+c)=ab+ac. After opening the brackets, subtract 20 from both sides of the equation and solve the equation to get all x related terms on one side of the equation and constant terms on the other side.

Complete step-by-step answer:
The equation given in the question is:
$6\left( 1-4x \right)+7\left( 2+5x \right)=53$
Now we will open the brackets by using the distributive nature of multiplication over addition and subtraction, i.e., a(b+c)=ab+ac or a(b-c)=ab-ac. On doing so, we get
$6-24x+14+35x=53$
$\Rightarrow 11x+20=53$
We know that an equation remains valid if we add or subtract the same number both in the Left Hand Side (LHS) and Right Hand Side (RHS). Therefore, we should subtract a number on both sides such that only the term with x remains on the LHS. So, we will subtract 20 from both sides of the equation.
$11x+20-20=53-20$
$\Rightarrow 11x=33$
Now we will divide both sides of the equation by 11. On doing so, we get
$\dfrac{11}{11}x=\dfrac{33}{11}$
$\Rightarrow x=3$

Note: You should remember that multiplying, adding, subtracting, or dividing the LHS and RHS of an equation by the same number gives other equation which is true, however you should not divide both sides of an equation by 0, as that would give non determinate values on the both sides of the equation. The possible mistakes in this question are making mistakes in sign of terms while opening the brackets. Often when students see simple questions, they calculate in their minds and skip steps.