ok heres another i don't get 3/4 (3x-1/2)-2/3<1/3
Try to solve it as you would any other equation.
Im not good at algebra so i don't know what to do?
You won't get any better at algebra until you try to solve equations.
Show us what you think, and someone will be glad to help you.
To solve the inequality 3/4(3x - 1/2) - 2/3 < 1/3, follow these steps:
Step 1: Distribute the fraction 3/4 to the expression inside the parentheses:
(3/4) * (3x - 1/2) - 2/3 < 1/3
This gives us:
(9x/4 - 3/8) - 2/3 < 1/3
Step 2: Simplify the expression in the parentheses:
To add or subtract fractions, we need a common denominator. The common denominator for 8 and 3 is 24. Multiply the fractions by appropriate factors to obtain the common denominator:
(9x/4 - 3/8) - (2/3 * 8/8) < 1/3
(9x/4 - 3/8) - 16/24 < 1/3
(9x/4 - 3/8) - 2/3 < 1/3
Now, let's simplify this expression:
(9x/4 - 3/8) - 16/24 < 1/3
(9x/4 - 3/8) - 2/3 < 1/3
Step 3: Combine like terms:
To subtract fractions, we need a common denominator. The common denominator for 24 and 3 is 24. Multiply the fractions by appropriate factors to obtain the common denominator:
(9x/4 - 3/8) - (2/3 * 8/8) < 1/3
(9x/4 - 3/8) - 16/24 < 1/3
Now, let's simplify this expression:
(9x/4 - 3/8) - 16/24 < 1/3
(9x/4 - 3/8) - 2/3 < 1/3
Step 4: Combine numerators into a single fraction:
Combine the numerators into a single fraction and keep the common denominator:
((9x - 3)/8) - 16/24 < 1/3
Step 5: Find a common denominator for all fractions:
Since the denominators are already the same, we can proceed to the next step.
Step 6: Perform the subtraction and simplify:
((9x - 3)/8) - 16/24 < 1/3
Combine the fractions on the left side:
((9x - 3)/8) - (2/3) < 1/3
To subtract fractions, we need a common denominator. The common denominator is 24. Multiply the fractions by appropriate factors to obtain the common denominator:
((9x - 3)/8) - (2/3 * 8/8) < 1/3
((9x - 3)/8) - 16/24 < 1/3
Now, let's simplify this expression:
((9x - 3)/8) - 16/24 < 1/3
((9x - 3)/8) - 2/3 < 1/3
Multiply all the terms on both sides by the common denominator to eliminate fractions:
24 * ((9x - 3)/8) - 24 * (2/3) < 24 * (1/3)
24(9x - 3)/8 - 16 < 8
3(9x - 3) - 16 < 8
Step 7: Simplify the expression:
27x - 9 - 16 < 8
27x - 25 < 8
Step 8: Solve for x:
27x < 8 + 25
27x < 33
To isolate x, divide both sides of the inequality by 27:
x < 33/27
x < 11/9
Therefore, the solution to the inequality 3/4(3x - 1/2) - 2/3 < 1/3 is x < 11/9.