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
Part A:
To solve the equation ax - 5 = 18, we want to isolate x on one side of the equation.
First, we can add 5 to both sides of the equation to get rid of the -5 on the left side:
ax - 5 + 5 = 18 + 5
This simplifies to:
ax = 23
Now, we want to solve for x by getting rid of the coefficient a. We can do this by dividing both sides of the equation by a:
(ax) / a = 23 / a
On the left side, the a's cancel out, leaving us with just x:
x = 23 / a
So 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.
First, we can add 5 to both sides of the inequality to get rid of the -5 on the left side:
ax - 5 + 5 > 18 + 5
This simplifies to:
ax > 23
Now, we want to solve for x by getting rid of the coefficient a. We can do this by dividing both sides of the inequality by a. However, we need to be careful. If a is negative, dividing by a will flip the inequality sign.
If a is positive:
(ax) / a > 23 / a
On the left side, the a's cancel out:
x > 23 / a
So if a is positive, the solution to the inequality is x > 23 / a.
If a is negative:
(ax) / a < 23 / a
On the left side, the a's cancel out, but the inequality sign flips:
x < 23 / a
So if a is negative, the solution to the inequality is x < 23 / a.
Therefore, the solution to the inequality ax - 5 > 18, depending on the value of a, is either x > 23 / a (if a > 0) or x < 23 / a (if a < 0).
Part A:
To solve the equation ax - 5 = 18, we can follow these steps:
Step 1: Add 5 to both sides of the equation to isolate the variable on the left side:
ax - 5 + 5 = 18 + 5
This simplifies to:
ax = 23
Step 2: Divide both sides of the equation by 'a' to solve for x:
(ax) / a = 23 / a
This simplifies to:
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 can follow these steps:
Step 1: Add 5 to both sides of the inequality to isolate the variable on the left side:
ax - 5 + 5 > 18 + 5
This simplifies to:
ax > 23
Step 2: Divide both sides of the inequality by 'a', but be cautious if 'a' is negative. If 'a' is negative, we need to flip the inequality sign:
If a > 0:
(ax) / a > 23 / a
This simplifies to:
x > 23 / a
If a < 0:
(ax) / a < 23 / a
This simplifies to:
x < 23 / a
So, based on the value of 'a', the solution to the inequality ax - 5 > 18 can be:
If a > 0, then x > 23 / a.
If a < 0, then x < 23 / a.