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3x≤23 OR 4x+26≥6 find x

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Final answer:

To solve the system of inequalities 3x≤23 OR 4x+26≥6, we solve each inequality separately, giving x≥7.67 and x≥-5, respectively. The solution is the union of both, meaning x can be any number within the range of those two solutions.

Step-by-step explanation:

When solving the system of inequalities 3x≤23 OR 4x+26≥6, we need to find the set of all possible values of x that satisfy at least one of these inequalities. To do so, let's solve each inequality separately.

For the inequality 3x≤23:

1. Divide both sides by 3 to isolate x: x ≤ 23 / 3

2. Calculate the result: x ≤ 7.67

Now, for the inequality 4x+26≥6:

1. Subtract 26 from both sides of the inequality: 4x ≥ 6 - 26

2. Simplify the right side: 4x ≥ -20

3. Divide both sides by 4 to isolate x: x ≥ -5

The solution to the system is the union of the two solutions since 'OR' connects the inequalities. This results in:

x ≥ -5 OR x ≤ 7.67

This means x can be any number greater than or equal to -5 as well as any number less than or equal to 7.67. Therefore, any such values for x would make at least one of the inequalities true.

User Jhnath
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