14x - 6x + 4 ≤ 35 + 1
Step 1: Simplify by combining like terms.
The like terms in this case are 14x and -6x on the left side and 35 and 1 on the right side.
14x - 6x = 8x
35 + 1 = 36
8x + 4 ≤ 36
8x + 4 ≤ 36
Step 2: Isolate the term with the variable.
To solve an inequality, you must isolate the variable. This is done by removing all other terms from that particular side of the equation as a first step.
In order to isolate the variable, x, we must subtract 4 from both sides.
8x + 4 - 4 = 8x
36 - 4 = 32
8x ≤ 32
8x ≤ 32
Step 3: Remove the coefficient from the variable.
Since we only want 1x, not 8x, we must remove the coefficient of 8 from x.
This can be done by dividing both sides by 8.
8x ÷ 8 = x
32 ÷ 8 = 4
x ≤ 4
x ≤ 4
This is the solution to the inequality!
Now for graphing!
When graphing inequalities, keep in mind the following rules:
- Shade to the above the line for "greater than" (≥ or >)
- Shade to the below the line for "less than" (≤ or <)
- Use a dashed line when the inequality not equal to (> or <)
- Use a solid line when the inequality can be equal to (≥ or ≤)
In this case, we would shade below the line and use a solid line.
This is because x is "less than" "or equal to" 4.
The "less than" part means shading below the line and "or equal to" part means using a solid line.
Final answer:
The solution to the inequality is x ≤ 4.
When you are graphing this, use a solid line and shading below the line.
Hope this helps!
