The equation is z = 8 + 6x – px and you’re solving for x.
The correct answer and explanation is:
Let’s start with the equation: z=8+6x−pxz = 8 + 6x – px
We want to solve for xx.
Step 1: Group the xx terms together.
Notice that both 6x6x and −px-px involve xx, so we can factor it out: z=8+x(6−p)z = 8 + x(6 – p)
Step 2: Isolate xx.
Subtract 8 from both sides to move constants to the left side: z−8=x(6−p)z – 8 = x(6 – p)
Step 3: Solve for xx.
Divide both sides by (6−p)(6 – p), assuming 6−p≠06 – p \neq 0: x=z−86−px = \frac{z – 8}{6 – p}
Final solution:
x=z−86−p\boxed{x = \frac{z – 8}{6 – p}}
Explanation:
This equation z=8+6x−pxz = 8 + 6x – px has xx terms on the right side combined with constants and parameters pp and zz. The first step to solving for xx is to group like terms. Since 6x6x and −px-px both multiply xx, factoring xx simplifies the expression to x(6−p)x(6-p).
After factoring, isolate xx by moving the constant term 8 to the left side with subtraction. The equation becomes z−8=x(6−p)z – 8 = x(6 – p).
Finally, to get xx alone, divide both sides by 6−p6 – p. This division step assumes 6−p≠06 – p \neq 0 because division by zero is undefined. If p=6p = 6, the equation would not be solvable for xx in this form.
This process illustrates a basic algebraic technique: combining like terms, isolating variables, and solving linear equations. It’s common in problems involving linear relationships where parameters affect the slope or coefficients of variables.
If you have specific values for zz and pp, you can substitute them in the final formula to get a numeric value for xx. Otherwise, the expression above is the general solution for xx in terms of zz and pp.