Solve for [tex]$x$[/tex]. [tex]$2(4x+5)-3=5x(2+1)$[/tex]
Answer (2)
Expand both sides of the equation: 2 ( 4 x + 5 ) − 3 = 8 x + 7 and 5 x ( 2 + 1 ) = 15 x .
Set up the equation: 8 x + 7 = 15 x .
Isolate x: 7 = 7 x .
Solve for x: x = 1 . The solution is 1 .
Explanation
Problem Analysis We are given the equation 2 ( 4 x + 5 ) − 3 = 5 x ( 2 + 1 ) and asked to solve for x .
Expanding Both Sides First, we expand both sides of the equation: 2 ( 4 x + 5 ) − 3 = 8 x + 10 − 3 = 8 x + 7 5 x ( 2 + 1 ) = 5 x ( 3 ) = 15 x
Isolating x Now we have the equation 8 x + 7 = 15 x . We want to isolate x on one side of the equation. Subtract 8 x from both sides: 8 x + 7 − 8 x = 15 x − 8 x 7 = 7 x
Solving for x Finally, divide both sides by 7 to solve for x :
7 7 = 7 7 x 1 = x
Final Answer Therefore, the solution to the equation is x = 1 .
Examples
In real-world scenarios, solving linear equations like this can help determine the break-even point in business. For example, if x represents the number of units you need to sell to make your revenue equal your costs, setting up and solving an equation helps you find that critical value. Understanding how to manipulate and solve these equations is fundamental in many areas of finance and economics.
The solution for x in the equation 2 ( 4 x + 5 ) − 3 = 5 x ( 2 + 1 ) is x = 1 . We expanded both sides, rearranged the equation, and solved for x . The steps led to determining that x equals 1.
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