Question

How do you solve $ - 4(2x + 7) = 2x + 18$ ?

Answer 1

Hint: We will first simplify the left-hand side of the equation by using the distributive property. According to the distributive property, the product of a number with the sum of two other numbers is equal to the product of that number with the first number plus the product of that number with the second number, that is, $a(b + c) = ab + ac$ . After simplifying the left-hand side, we will rearrange the equation such that all the terms containing “x” are on one side and the constant terms are present on the other side. Then we will find the value of x by applying the given arithmetic operations.

Complete step-by-step solution:
We are given that $ - 4(2x + 7) = 2x + 18$
On applying the distributive property on the left-hand side, we get –
$\Rightarrow - 8x - 28 = 2x + 18$
We will take 2x to the left-hand side and 28 to the right-hand side –
$
   \Rightarrow - 8x - 2x = 18 + 28 \\
   \Rightarrow - 10x = 46 \\
 $
Now, we will take -10 to the right-hand side –
$\Rightarrow x = - \dfrac{{46}}{{10}}$
We will simplify the obtained fraction by canceling out the common factors or we can also write the fraction in decimal form –
$\Rightarrow x = - \dfrac{{23}}{5}\,or\,x = - 4.6$
Hence, when $ - 4(2x + 7) = 2x + 18$ , we get $x = - \dfrac{{23}}{5}\,or\,x = - 4.6$ .

Note: In this question, we are given an algebraic expression containing an unknown variable quantity “x” linked to the constant numerical values via arithmetic operations like addition, subtraction, multiplication and division. We know that for finding the values of “n” unknown variable quantities, we need “n” number of equations. In this question, we have exactly one equation to find the value of one unknown quantity, so its value is obtained easily as shown above.