Part A:
To solve the equation ax - 5 = 18, we want to isolate x.
Adding 5 to both sides of the equation:
ax - 5 + 5 = 18 + 5
ax = 23
To isolate x, we divide both sides of the equation by a:
(ax) / a = 23 / a
x = 23/a
Therefore, the solution to the equation is x = 23/a.
Part B:
To solve the inequality ax - 5 > 18, we want to find the values of x that make the inequality true.
Adding 5 to both sides of the inequality:
ax - 5 + 5 > 18 + 5
ax > 23
To isolate x, we divide both sides of the inequality by a. However, we need to consider the sign of a. If a is positive, we can divide without changing the inequality. If a is negative, we need to reverse the inequality sign.
If a > 0:
(ax) / a > 23 / a
x > 23/a
If a < 0:
(ax) / a < 23 / a
x < 23/a
Therefore, the solution to the inequality ax - 5 > 18 is x > 23/a if a > 0, and x < 23/a if a < 0.
Answer to Questions:
1. To represent all the solutions of the inequality ax - 5 > 18 on a number line, we would draw an open circle at 23/a (if a > 0) or a closed circle at 23/a (if a < 0), and shade the region to the right (if a > 0) or to the left (if a < 0) of the circle.
2. The difference between solving an equation and an inequality is that solving an equation finds the specific value for the variable that makes the equation true, while solving an inequality finds the range of values for the variable that makes the inequality true. In an equation, there is usually only one solution, while in an inequality, there can be infinitely many solutions or a range of solutions.
Solve 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.
5 answers
can you simplify the writing
Certainly! Here is the simplified writing:
Part A:
Equation: ax - 5 = 18
Solution:
1. Add 5 to both sides:
ax - 5 + 5 = 18 + 5
ax = 23
2. Divide both sides by a:
(ax) / a = 23 / a
x = 23/a
The solution to the equation is x = 23/a.
Part B:
Inequality: ax - 5 > 18
Solution:
1. Add 5 to both sides:
ax - 5 + 5 > 18 + 5
ax > 23
2. Consider the sign of a:
- If a > 0, we can divide both sides by a:
(ax) / a > 23 / a
x > 23/a
- If a < 0, we divide both sides by a and reverse the inequality sign:
(ax) / a < 23 / a
x < 23/a
The solution to the inequality is x > 23/a if a > 0, and x < 23/a if a < 0.
Answers to Questions:
1. To represent all the solutions of ax - 5 > 18 on a number line, mark an open circle at 23/a (if a > 0) or a closed circle at 23/a (if a < 0), and shade the region to the right (if a > 0) or left (if a < 0) of the circle.
2. The difference between solving an equation and an inequality is that an equation finds a specific value for the variable that satisfies the equation, while an inequality finds a range of values for the variable that fulfill the inequality. Equations usually have one solution, while inequalities can have infinitely many solutions or a range of solutions.
Part A:
Equation: ax - 5 = 18
Solution:
1. Add 5 to both sides:
ax - 5 + 5 = 18 + 5
ax = 23
2. Divide both sides by a:
(ax) / a = 23 / a
x = 23/a
The solution to the equation is x = 23/a.
Part B:
Inequality: ax - 5 > 18
Solution:
1. Add 5 to both sides:
ax - 5 + 5 > 18 + 5
ax > 23
2. Consider the sign of a:
- If a > 0, we can divide both sides by a:
(ax) / a > 23 / a
x > 23/a
- If a < 0, we divide both sides by a and reverse the inequality sign:
(ax) / a < 23 / a
x < 23/a
The solution to the inequality is x > 23/a if a > 0, and x < 23/a if a < 0.
Answers to Questions:
1. To represent all the solutions of ax - 5 > 18 on a number line, mark an open circle at 23/a (if a > 0) or a closed circle at 23/a (if a < 0), and shade the region to the right (if a > 0) or left (if a < 0) of the circle.
2. The difference between solving an equation and an inequality is that an equation finds a specific value for the variable that satisfies the equation, while an inequality finds a range of values for the variable that fulfill the inequality. Equations usually have one solution, while inequalities can have infinitely many solutions or a range of solutions.
make the writing smaller
Part A:
Equation: ax - 5 = 18
Solution:
1. ax - 5 + 5 = 18 + 5
ax = 23
2. (ax) / a = 23 / a
x = 23/a
Part B:
Inequality: ax - 5 > 18
Solution:
1. ax - 5 + 5 > 18 + 5
ax > 23
2. - If a > 0: (ax) / a > 23 / a, x > 23/a
- If a < 0: (ax) / a < 23 / a, x < 23/a
Answers to Questions:
1. On a number line, mark an open circle at 23/a (if a > 0) or a closed circle at 23/a (if a < 0), and shade the region to the right (if a > 0) or left (if a < 0) of the circle.
2. Solving an equation finds a specific value for the variable, while solving an inequality finds a range of values that fulfill the inequality. Equations usually have one solution, while inequalities can have infinitely many or a range of solutions.
Equation: ax - 5 = 18
Solution:
1. ax - 5 + 5 = 18 + 5
ax = 23
2. (ax) / a = 23 / a
x = 23/a
Part B:
Inequality: ax - 5 > 18
Solution:
1. ax - 5 + 5 > 18 + 5
ax > 23
2. - If a > 0: (ax) / a > 23 / a, x > 23/a
- If a < 0: (ax) / a < 23 / a, x < 23/a
Answers to Questions:
1. On a number line, mark an open circle at 23/a (if a > 0) or a closed circle at 23/a (if a < 0), and shade the region to the right (if a > 0) or left (if a < 0) of the circle.
2. Solving an equation finds a specific value for the variable, while solving an inequality finds a range of values that fulfill the inequality. Equations usually have one solution, while inequalities can have infinitely many or a range of solutions.
1 answer