Question

Which is a correct first step in solving the inequality –4(2x – 1) > 5 – 3x?

Answer 1

The first step in solving the inequality is to distribute –4 to get -8x + 4 > 5 - 3x

Solution:

Given inequality is:

$-4(2x - 1) > 5 - 3x$

The first step in solving the inequality is to distribute -4 to terms inside the bracket in left side of equation

This is done according to BODMAS rule

According to Bodmas rule, if an expression contains brackets ((), {}, []) we have to first solve or simplify the bracket followed by of (powers and roots etc.), then division, multiplication, addition and subtraction from left to right

Thus in given inequality, brackets has to solved first

This is done by using distributive property

a(b + c) = ab + bc

Therefore,

$-4(2x - 1) = (-4 \times 2x) +(-4 \times -1) = -8x + 4$

Thus, the inequality becomes,

$-4(2x - 1) > 5 - 3x\\\\-8x + 4>5-3x\\\\-5x>1\\\\x$

Thus solution to given inequality is found