To graph the inequalities 5(g+4) > 15 and -1.3 >= 2.9 - 0.5r, you first solve for g and r respectively, and then plot the solutions on a number line, shading the area that represents the solution set.
To graph the inequalities, we first need to solve for the variables and then plot the solutions on a number line.
Solving the first inequality:
5(g+4) > 15
Divide both sides by 5: g + 4 > 3
Subtract 4 from both sides: g > -1
Graph this on a number line: we draw an open circle at -1 and shade to the right, indicating all numbers greater than -1.
Solving the second inequality:
-1.3 ≥ 2.9 - 0.5r
Add 1.3 to both sides: 0 ≥ 2.9 + 1.3 - 0.5r
Simplify the constants: 0 ≥ 4.2 - 0.5r
Subtract 4.2 from both sides: -4.2 ≥ -0.5r
Divide by -0.5 (and flip the inequality sign): r ≥ 8.4
Graph this on a number line: we draw a closed circle at 8.4 and shade to the right, indicating all numbers greater than or equal to 8.4.
Both graphs represent the range of solutions for the given inequalities.
Both the graphs are attached below.