Question 2.4.2: Solve for x: 3(x - 5) + 4 = 13....
Solve for x: 3(x – 5) + 4 = 13.
Step 1:
We start by applying the distributive property to the left side of the equation, which means we need to multiply 3 by both terms inside the parentheses: 3x and -15. This gives us 3x - 45 + 4 = 13.
Step 2:
Next, we simplify the left side of the equation by combining like terms. The -45 and +4 can be combined to give us -41. So now we have 3x - 41 = 13.
Step 3:
To isolate the variable x, we want to get rid of the -41. We can do this by adding 41 to both sides of the equation: 3x - 41 + 41 = 13 + 41. This simplifies to 3x = 54.
Step 4:
Finally, to solve for x, we divide both sides of the equation by 3. This gives us (1/3)(3x) = (1/3)(54), which simplifies to x = 18.
So the solution to the equation is x = 18.
Final Answer
Our first step will be to apply the distributive property to the left side of the equation:
\begin{aligned}3 x-15+4 & =13 & & \text { Distributive property } \\ 3x-11&=13&& \text { Simplify the left side } \\ 3 x-11+ 1 1 & =13+ 1 1 & & \text { Add } 1 1 \text { to both sides } \\3 x & =24 & & \\1 (3 x) & =\frac{ 1 }{ 3 }(24) & & \text { Multiply both sides by } \frac{1}{3} \\x & =8 & &\end{aligned}
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