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Solve each inequality. Write the solution set in interval notation and graph it.$$2(5 x-6)>4 x-15+6 x$$
$0>-3$
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
McMaster University
Harvey Mudd College
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solve the inequality. Two times five x minus six is greater than four x minus 15 plus six x. Let's rewrite the inequality without the parentheses, using the distributive property on the left and combining like terms at the same time on the right. Two times five x is 10 x two times negative. Six is negative 12 and this is greater than four x plus six x, which is 10 X minus 15. Now we haven't inequality. That's 10 x minus 12 is greater than 10 x minus 15. Watch what happens when we try to isolate the variable toe one side of the inequality. Subtract 10 x from both sides. This leaves us with negative 12 on the left is greater than negative 15 on the right. Now there is no more X variable. It cancelled itself out, and as a result, we have a true statement. Negative 12 is greater than negative 15. What this means is that no matter what value we substitute into this inequality for X, it will always be true. The solution set for this inequality is all rial numbers, an interval notation. We would represent this with an open parentheses. Ito open the interval at negative infinity and we would close it at positive infinity, also with the parentheses, E and on our number line, we're going to include the entire number line from negative infinity all the way to positive infinity because all values make this true.
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