Respuesta :
Answer:
9 + 7x – 12 = 3x + 5 – 4(2 – x) Solution: x = all real numbers
12 + 7x – 9 = 3x + 5 – 4(2 - x) Solution: no solution
4 – 9x = 3 – 10x - (7 - x) Solution: no solution
5(3 – x) + 8x = 3(x + 5) Solution: x = all real numbers
5(3 - x) = 3(× + 5 ) Solution: x = 0
Explanation:
To match the expressions, we solve for x in each case.
Equation 1. 9 + 7x – 12 = 3x + 5 – 4(2 – x)
Expanding both sides of the equation gives
[tex]\begin{gathered} 9+7x-12=3x+5-8+4x \\ \end{gathered}[/tex]simplifying gives
[tex]7x-3=-3+7x[/tex]adding 3 to both sides gives
[tex]7x=7x[/tex]which has infinitely many solutions (meaning all real numbers)
Equation 2. 12 + 7x – 9 = 3x + 5 – 4(2 - x)
Expanding both sides gives
[tex]12+7x-9=3x+5-8+4x[/tex]simplifying gives
[tex]3+7x=7x-3[/tex]subtracting 7x from both sides gives
[tex]3=-3[/tex]which cannot be true, and therefore, the equation has no solutions.
Equation 3. 4 – 9x = 3 – 10x - (7 - x)
Expanding both sides of the equation gives
[tex]4-9x=3-10x-7+x[/tex]simplifying gives
[tex]4-9x=-9x-4[/tex]adding 9x to both sides gives
[tex]4=-4[/tex]which cannot be true, and therefore, the equation has no solutions.
Equation 4. 5(3 – x) + 8x = 3(x + 5)
Expanding both sides of the equation gives
[tex]15-5x+8x=3x+15[/tex]simplifying gives
[tex]15+3x=3x+15[/tex]which has infinitely many solutions (any value of x you pick will satisfy the equation above)
Equation 5. 5(3 - x) = 3(x + 5 )
Expanding both sides of the equation gives
[tex]15-5x=3x+15[/tex]subtracting 15 from both sides gives
[tex]-5x=3x[/tex]which has no solutions (no value of x you pick will satisfy the equation).
Hence to summarise, the answers are the following.
9 + 7x – 12 = 3x + 5 – 4(2 – x) Solution: x = all real numbers
12 + 7x – 9 = 3x + 5 – 4(2 - x) Solution: no solution
4 – 9x = 3 – 10x - (7 - x) Solution: no solution
5(3 – x) + 8x = 3(x + 5) Solution: x = all real numbers
5(3 - x) = 3(× + 5 ) Solution: x = 0
