QuestionSolve the equation $7(3x-5)=3(x+2)-19$ and express the answer as an integer, simplified fraction, or decimal (2 decimal places).

Studdy Solution

STEP 1

Assumptions1. The equation is linear and in the form of $ax + b = cx + d$ . We are solving for the variable $x$
3. The solution should be expressed as an integer, a simplified fraction, or a decimal rounded to two decimal places

STEP 2

First, we need to distribute the numbers outside the parentheses on both sides of the equation.
$7(x -5) =21x -35$ $(x +2) =x +6$ So, the equation becomes $21x -35 =x +6$

STEP 3

Next, we need to isolate $x$ by moving all terms with $x$ to one side of the equation and constants to the other side.Subtract $3x$ from both sides $21x -3x =35 +6$ This simplifies to $18x =41$

STEP 4

Finally, to solve for $x$ , divide both sides of the equation by $18$ $x = \frac{41}{18}$ This is already a simplified fraction, so no further simplification is needed.
So, the solution to the equation is $x = \frac{41}{18}$ .

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