Part A:
To solve the equation ax - 5 = 18, we need to isolate x.
Step 1: Add 5 to both sides of the equation:
ax - 5 + 5 = 18 + 5
ax = 23
Step 2: Divide both sides of the equation by a to solve for x:
(ax)/a = 23/a
x = 23/a
Therefore, the solution to the equation ax - 5 = 18 is x = 23/a.
Part B:
To solve the inequality ax - 5 > 18, we need to isolate x.
Step 1: Add 5 to both sides of the inequality:
ax - 5 + 5 > 18 + 5
ax > 23
Step 2: Divide both sides of the inequality by a to solve for x:
(ax)/a > 23/a
x > 23/a
Therefore, the solution to the inequality ax - 5 > 18 is x > 23/a.
1. To represent the solutions on a number line, we would mark a point at 23/a and draw an arrow to the right, as the inequality states that x should be greater than 23/a.
2. The main difference between solving an equation and an inequality is that when solving an equation, we are finding a specific value for the variable that makes the equation true. In contrast, when solving an inequality, we are looking for a range of values for the variable that make the inequality true.
olve the equation and inequality for x.
Part A: Solve the equation showing all steps.
ax−5=18
Part B: Solve the inequality showing all steps.
ax−5>18
Answer these Questions:
1. Describe the number line set up that would show all of the solutions for the inequality in Part B.
2. State the difference between solving an equation and an inequality.
(4 points)
3 answers
make it more ssimple
Part A:
ax - 5 = 18
Add 5 to both sides:
ax = 23
Divide both sides by a:
x = 23/a
The solution to the equation is x = 23/a.
Part B:
ax - 5 > 18
Add 5 to both sides:
ax > 23
Divide both sides by a:
x > 23/a
The solution to the inequality is x > 23/a.
1. On a number line, mark a point at 23/a and draw an arrow to the right to represent all values of x that are greater than 23/a.
2. The main difference between solving an equation and an inequality is that when solving an equation, we find a specific value for the variable that satisfies the equation, whereas when solving an inequality, we find a range of values for the variable that satisfy the inequality.
ax - 5 = 18
Add 5 to both sides:
ax = 23
Divide both sides by a:
x = 23/a
The solution to the equation is x = 23/a.
Part B:
ax - 5 > 18
Add 5 to both sides:
ax > 23
Divide both sides by a:
x > 23/a
The solution to the inequality is x > 23/a.
1. On a number line, mark a point at 23/a and draw an arrow to the right to represent all values of x that are greater than 23/a.
2. The main difference between solving an equation and an inequality is that when solving an equation, we find a specific value for the variable that satisfies the equation, whereas when solving an inequality, we find a range of values for the variable that satisfy the inequality.
5 answers