Rewrite the equation (4x / 3x − 12) + 3 = 10 in two equations joined by “and.”
(4x / 3x − 12) + 3 = 10 can be rewritten as:
(4x / 3x − 12) = 7 and 3 = 10
To rewrite the equation (4x / 3x - 12) + 3 = 10 in two equations joined by "and," we need to isolate each side of the equation. Here are the steps:
Step 1: Subtract 3 from both sides to move it to the right side of the equation:
(4x / 3x - 12) = 10 - 3
Simplified:
(4x / 3x - 12) = 7
Step 2: Multiply both sides by 3x to eliminate the fraction on the left side:
3x * (4x / 3x - 12) = 7 * 3x
Simplified:
4x - 36x = 21x
Step 3: Separate the equation into two equations:
4x = 21x + 36x
Equations joined by "and":
4x = 57x
Therefore, the two equations joined by "and" are:
4x = 57x and (4x / 3x - 12) = 7
To rewrite the equation (4x / 3x - 12) + 3 = 10 in two equations joined by "and," we need to separate the equation into two distinct equations.
First, let's simplify the expression within the parentheses using the division rule:
(4x / 3x) - 12 + 3 = 10
Simplifying further, we can cancel out the common factor of 'x' in the numerator and denominator:
4/3 - 12 + 3 = 10
Now, let's combine like terms:
(4/3) - 9 + 3 = 10
To get rid of the fraction, we can multiply both sides of the equation by the denominator, which is 3:
3 * [(4/3) - 9 + 3] = 3 * 10
4 - 27 + 9 = 30
Simplifying the left side of the equation:
-14 = 30
Since -14 is not equal to 30, the equation is not true and there is no solution.
Therefore, rewriting the equation (4x / 3x - 12) + 3 = 10 in two equations joined by "and" would be:
(4/3) - 9 + 3 = 10 and -14 ≠ 30