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Solve the two-step equation.
$\begin{array}{l}
-\frac{2}{3} x-\frac{21}{4}=\frac{27}{4} \\
x=\square
\end{array}$
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Answer (1)
Add 4 21 to both sides: − 3 2 x = 4 27 + 4 21 .
Simplify the right side: − 3 2 x = 12 .
Multiply both sides by − 2 3 : x = 12 ⋅ ( − 2 3 ) .
Simplify to find the value of x : x = − 18 .
Explanation
Understanding the Problem We are given the equation − 3 2 x − 4 21 = 4 27 Our goal is to isolate x and find its value.
Isolating the x term First, we add 4 21 to both sides of the equation to get rid of the constant term on the left side: − 3 2 x − 4 21 + 4 21 = 4 27 + 4 21 − 3 2 x = 4 27 + 4 21
Simplifying the equation Now, we simplify the right side by adding the two fractions: − 3 2 x = 4 27 + 21 − 3 2 x = 4 48 − 3 2 x = 12
Solving for x To solve for x , we multiply both sides of the equation by − 2 3 (which is the reciprocal of − 3 2 ): − 3 2 x × ( − 2 3 ) = 12 × ( − 2 3 ) x = 12 × ( − 2 3 )
Finding the value of x Finally, we simplify the right side to find the value of x :
x = 2 12 × ( − 3 ) x = 2 − 36 x = − 18
Examples
Imagine you're baking a cake and need to adjust a recipe. If the recipe calls for a certain amount of flour, but you only want to make a fraction of the cake, you'll need to solve a similar equation to figure out how much flour to use. This type of problem helps in scaling recipes, adjusting quantities in experiments, or calculating proportions in various real-life situations.
