lesson 6 sovle inequalities by adding or subtracting
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To solve inequalities by adding or subtracting, you follow the same basic steps as solving equations. Here are the steps:
1. Start by simplifying both sides of the inequality if needed.
2. Determine if you need to add or subtract a number to isolate the variable.
3. Add or subtract the same number to both sides of the inequality.
4. Simplify both sides of the inequality again if necessary.
5. If there is no more simplification to be done, check if there is a specific range of values that satisfies the inequality.
6. If there is a range of values, write the solution in interval notation or set notation, depending on the context of the problem.
Here are a few examples to illustrate the process:
Example 1:
Solve the inequality: 2x - 3 > 5
1. Simplify both sides: 2x - 3 > 5
2. Add 3 to both sides: 2x > 8
3. Simplify: x > 4
4. The solution is x > 4.
Example 2:
Solve the inequality: 3y + 7 < 22
1. Simplify both sides: 3y + 7 < 22
2. Subtract 7 from both sides: 3y < 15
3. Simplify: y < 5
4. The solution is y < 5.
Example 3:
Solve the inequality: -4z + 8 ≥ 16
1. Simplify both sides: -4z + 8 ≥ 16
2. Subtract 8 from both sides: -4z ≥ 8
3. Simplify: -4z ≥ 8
4. Divide both sides by -4, but remember to flip the inequality sign when dividing by a negative number: z ≤ -2
5. The solution is z ≤ -2.
Note: It is important to remember to flip the inequality sign when multiplying or dividing by a negative number.