Question

PLEASE EXPLAIN IN DETAILS HOW TO SOLVE LINEAR INEQUALITIES. Heres an example problem. Please solve and show your steps/explain.

Answer 1

Answer:

$x \geq -91/2$

Step-by-step explanation:

$6(x+8) \geq -43 + 4x$

Resolving Parenthesis

$6x+48 \geq -43 + 4x$

Collecting like terms

$6x - 4 x \geq -43-48$

$2x \geq -91$

Dividing both sides by 2

$x \geq -91/2$

Answer 2

Answer:

x ≥ - 91 / 2

Step-by-step explanation:

In this sample problem, the first thing we want to do is expand the part in parenthesis through the distributive property. This will make the simplification process easier. Another approach would be to divide either side by x + 8, but let's try the first.

Approach 1 : $6(x+8) = 6x + 6 8 = 6x + 48$

$6x + 48 \geq - 43+4x$ - so we have this simplified expression. We now want to isolate x, so let's combine common terms here. Start by subtracting 6x from either side,

$48 \geq - 43-2x$ - now add 43 to either side,

$91\geq -2x$ - remember that dividing or multiplying a negative value changed the inequality sign. Dividing - 2 on either side, the sign changes to greater than or equal to, with respect to x,

$- 91 / 2 \leq x$, or in other words $x \geq - 91 / 2$. This is our solution.