Solve the inequality
4x−4<24
The Correct Answer and Explanation is :
To solve the inequality ( 4x – 4 < 24 ), follow these steps:
Step 1: Isolate the variable term
Start by getting rid of the constant term on the left side of the inequality:
[
4x – 4 < 24
]
Add 4 to both sides to eliminate the -4:
[
4x < 24 + 4
]
[
4x < 28
]
Step 2: Solve for ( x )
Now, divide both sides of the inequality by 4 to isolate ( x ):
[
x < \frac{28}{4}
]
[
x < 7
]
Final Answer:
The solution to the inequality is ( x < 7 ).
Explanation:
This inequality can be solved using basic algebraic steps, similar to solving an equation. The key difference with inequalities is the way we interpret the solution and how it affects the graph or possible values of ( x ).
The inequality ( 4x – 4 < 24 ) states that the expression ( 4x – 4 ) must be less than 24. The first step is to isolate ( x ) by undoing the subtraction. By adding 4 to both sides, we simplify the inequality to ( 4x < 28 ). The next step is to divide both sides by 4, which simplifies the inequality to ( x < 7 ). This tells us that the solution includes all values of ( x ) that are less than 7, but does not include 7 itself.
If you graph this inequality on a number line, you would have an open circle at 7 (to indicate that 7 is not included) and shade everything to the left of 7, representing all numbers less than 7.
In summary, solving inequalities is similar to solving equations but requires attention to the direction of the inequality sign. The solution ( x < 7 ) means any value of ( x ) smaller than 7 satisfies the original inequality.