Solving Inequalities Elementary Math Steps Examples Questions 2 5 <3 5. 2 5 <3 5 \cfrac {2} {5}<\cfrac {3} {5} 52 <53 . you can represent inequalities on a number line. recall, that x=5 x = 5 is an equation. the variable x x is only equal to 5. 5. in an equality, the value of x x can be many numbers. you can interpret and represent inequality statements on the number line. Summary. many simple inequalities can be solved by adding, subtracting, multiplying or dividing both sides until you are left with the variable on its own. but these things will change direction of the inequality: multiplying or dividing both sides by a negative number. swapping left and right hand sides.
Solving Inequalities Elementary Math Steps Examples Questions Example 2: solving linear inequalities. solve: 5x 4 \geq 26 5x − 4 ≥ 26. rearrange the inequality so that all the unknowns are on one side of the inequality sign. show step. in this case you need to add 4 4 to both sides. \begin {aligned} 5x 4&\geq26\\ 5x&\geq30 \end {aligned} 5x − 4 5x ≥ 26 ≥ 30. 3x 3 < 18 3. x < 6. solving this example required two steps (step one: subtract 8 from both sides; step two: divide both sides by 3). the result is the solved inequality x<6. the step by step procedure to solving example #2 is illustrated in figure 04 below. figure 04: how to solve an inequality: 3x 8<26. Solution: let ‘x’ be the number of months bruce needs to work. as we know, the amount already saved by bruce is $ 121. he earns $ 44 per month. the cost of the tablet is at least $ 561. after ‘x’ months of work, bruce will have $ (121 44x) now, the inequality representing the situation is: 121 44x ≥ 561. Solving linear inequalities with division. let’s see a few examples below to understand this concept. example 7. solve the inequality: 8x − 2 > 0. solution. first of all, add both sides of the inequality by 2. 8x – 2 2 > 0 2. 8x > 2. now, solve by dividing both sides of the inequality by 8 to get; x > 2 8. x > 1 4 example 8. solve the.
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