2/3(12x-21)-2x=4xdivided by 10
Solve for x?
8x-14-2x=4x/10
6x*10=4x+140
56x=140
x=140/56
three times a number, minus 6,is the same as two times a number, plus 3 find the numb
To solve this equation, we need to follow the order of operations (also known as PEMDAS), which stands for parentheses, exponents, multiplication/division (from left to right), and addition/subtraction (from left to right).
Let's break down the equation step by step:
1. Start by simplifying the expression inside the parentheses:
2/3(12x - 21) - 2x = 4x / 10
Multiply 2/3 by each term inside the parentheses:
(2/3) * 12x = (24x)/3
(2/3) * (-21) = (-14)/3
Substituting these values back into the equation, we get:
(24x)/3 - (-14)/3 - 2x = 4x / 10
Simplifying further, we have:
(24x - (-14))/3 - 2x = 4x / 10
2. Next, let's simplify the subtraction by changing the sign and turning it into addition:
(24x - (-14))/3 + 2x = 4x / 10
By changing the sign of "- (-14)", we get:
(24x + 14)/3 + 2x = 4x / 10
3. Now, let's simplify the right side of the equation:
The expression "4x/10" can be rewritten as "2x/5":
(24x + 14)/3 + 2x = 2x / 5
4. To eliminate the fractions, let's multiply both sides of the equation by the least common multiple (LCM) of the denominators, which in this case is 3 and 5:
Multiplying both sides by 3 * 5 = 15, we get:
15 * [(24x + 14)/3 + 2x] = 15 * (2x / 5)
The fractions cancel out, and we are left with:
15(24x + 14) + 30x = 6x
5. Distribute the 15 to each term inside the parentheses:
360x + 210 + 30x = 6x
6. Combine like terms on the left side of the equation:
390x + 210 = 6x
7. Subtract 6x from both sides to isolate the variable on one side:
390x + 210 - 6x = 0
Simplifying further, we have:
384x + 210 = 0
8. Subtract 210 from both sides:
384x + 210 - 210 = 0 - 210
Simplifying further, we have:
384x = -210
9. Finally, divide both sides by 384 to solve for x:
(384x)/384 = (-210)/384
The 384s cancel out, and we are left with:
x = -210/384
To simplify further, we can reduce the fraction (-210/384) by dividing both the numerator and the denominator by their greatest common divisor (GCD) which is 6:
x = -35/64
So, the solution to the equation is x = -35/64.