Questions: Solve the equation. 7+4(6-5x)=19-16x The solution is x= □ (Simplify your answer. Type an integer, proper fraction, or mixed number.)

$Solve the equation. 7+4(6-5x)=19-16x The solution is x= □ (Simplify your answer. Type an integer, proper fraction, or mixed number.)$

Transcript text: Solve the equation. \[ 7+4(6-5 x)=19-16 x \] The solution is $\mathrm{x}=$ $\square$ (Simplify your answer. Type an integer, proper fraction, or mixed number.)

Solution

Solution Steps

To solve the equation $7 + 4(6 - 5x) = 19 - 16x$, we will first expand the terms inside the parentheses and distribute the 4. Then, we will combine like terms and isolate the variable $x$ on one side of the equation to solve for it.

Step 1: Expand and Simplify the Equation

Start with the original equation: \[ 7 + 4(6 - 5x) = 19 - 16x \] Distributing the 4 gives: \[ 7 + 24 - 20x = 19 - 16x \] This simplifies to: \[ 31 - 20x = 19 - 16x \]

Step 2: Isolate the Variable

Next, we will isolate $x$ by moving all terms involving $x$ to one side and constant terms to the other side. Adding $20x$ to both sides results in: \[ 31 = 19 + 4x \] Subtracting 19 from both sides gives: \[ 12 = 4x \]

Step 3: Solve for $x$

Now, divide both sides by 4 to solve for $x$: \[ x = 3 \]