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Solve each inequality or compound inequality. Write the solution set in interval notation and graph it.$$7<\frac{5}{3} a+(-3)$$
$$(6, \infty)$$
Precalculus
Algebra
Chapter 2
Equations, Inequalities, and Problem Solving
Section 7
Solving Inequalities
Algebra Topics That are Reviewed at the Start of the Semester
Equations and Inequalities
Harvey Mudd College
University of Michigan - Ann Arbor
Idaho State University
Lectures
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In mathematics, the absolu…
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Solve each inequality. Gra…
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Solve each compound inequa…
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Solve each inequality. Wri…
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solve the inequality. Seven is less than 5/3 a plus. Negative. Three. To simplify this inequality, I'd like to start by rewriting it without the parentheses around the negative three. So this inequality can be rewritten as seven is less than 5/3 a minus three. From here, we can isolate the variable by undoing the subtraction of three and adding three to both sides. Seven plus three is 10 and 10 is less than 5/3 A. To isolate A, we need to undo the product of 5/3. To do that, let's multiply by the reciprocal. The reciprocal of 5/3 is three fits, so we're going to multiply both sides of the inequality by 3/5 which will leave us with three times 10. Divided by five is six on the left is less than 5/3 times 3/5 is one A on the right. Six is less than a is the equivalent inequality to a is greater than six. An interval notation. We would start with an open parentheses, e at six and close the interval at positive infinity and a parentheses e on our number line. That's an open circle at six and shaded to the right to include all values greater than six. Remember, we used parentheses and open circles to indicate the value is not included in the solution set.
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