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Solving One-Step Inequalities

Solving One-Step Inequalities 1.4 - Solution

arrow_back Return to Solving One-Step Inequalities
a
Inequalities can be solved in the same way as equations, by performing inverse operations on both sides until the variable is isolated. The only difference is that when you divide or multiply by a negative number, you must reverse the inequality sign. Here, we'll subtract both sides by 44 so the inequality sign doesn't change.
r+4<5r+4 < 5
r<1r < 1
This expression tells us that all values less than 11 will satisfy the inequality. Note that rr cannot be equal to 1,1, which we show with an open circle on the number line.
b
We solve the inequality by using inverse operations on both sides until the ww is isolated.
9+w>79+w > 7
w>-2w > \text{-} 2
This inequality tells us that all values greater than -2\text{-} 2 are solutions. Note that ww cannot equal -2,\text{-} 2, which we show with an open circle on the number line.
c
The variable mm can be isolated by subtracting 1111 from both sides of the inequality.
11+m1511+m\geq15
m4m\geq4
This expression tells us that all values greater than or equal to 44 will satisfy the inequality. Since mm can equal 4,4, we will mark it as a closed circle on the number line.
d
To solve the inequality we'll subtract ww from both sides to gather all ww-terms.
w52ww-5\leq2w
-5w\text{-}5\leq w
w-5w\geq\text{-}5
This inequality tells us that all values greater than or equal to -5\text{-} 5 will satisfy the inequality. Thus, -5\text{-}5 should be marked as an closed circle and the part to the right represents all values greater than -5.\text{-}5.