Solve the inequality symbolically. Express the solution set in interval notation.
To solve the inequality, isolate the variable on one side the inequality using the properties if inequalities.
First, use the distributive property to eliminate the parentheses on both sides of the equation.
-7(z-8) ≥ 4(9-2z)
-7z + 56 ≥ 36 – 8z (Simplify the right side.)
Add 8z to both sides so that all expressions containing a variable are on the left side.
-7z +56 ≥ 36 – 8z
z + 56 ≥ 36 (Add 8z to both sides)
To isolate z, subtract 56 form both sides.
z + 56 ≥ 36
z ≥ 56 ≥ 36
z ≥ -20 (Subtract)
Thus, the solution is the set of all real numbers greater than or equal to -20.
In interval notation, a square bracket is used to show that a number is part of the interval and a parenthesis is used to indicate that a number is not part of the interval.
Write the solution set is interval notation.