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Solve the equation. Check your solution\newline19=2(z+5)19=2-(z+5)\newline

Full solution

Q. Solve the equation. Check your solution\newline19=2(z+5)19=2-(z+5)\newline
  1. Rewrite Equation: Rewrite the equation to isolate the variable zz on one side.\newline19=2(z+5)19 = 2 - (z + 5)
  2. Move Terms Left: Move the term (z+5)(z + 5) to the left side by adding (z+5)(z + 5) to both sides of the equation.\newline19+(z+5)=219 + (z + 5) = 2
  3. Combine Like Terms: Combine like terms on the left side. 19+z+5=219 + z + 5 = 2
  4. Simplify Left Side: Simplify the left side by adding the numbers. 24+z=224 + z = 2
  5. Subtract 2424: Subtract 2424 from both sides to isolate zz.\newline24+z24=22424 + z - 24 = 2 - 24
  6. Simplify Solution: Simplify both sides. \newlinez=22z = -22
  7. Check Solution: Check the solution by substituting z=22z = -22 back into the original equation.19=2((22)+5)19 = 2 - ((-22) + 5)
  8. Simplify Right Side: Simplify the right side of the equation. 19=2(22+5)19 = 2 - (-22 + 5)
  9. Combine Numbers: Combine the numbers inside the parentheses.\newline19=2(17)19 = 2 - (-17)
  10. Simplify Right Side: Subtracting a negative is the same as adding the positive equivalent.\newline19=2+1719 = 2 + 17
  11. Simplify Right Side: Subtracting a negative is the same as adding the positive equivalent.\newline19=2+1719 = 2 + 17 Simplify the right side by adding the numbers.\newline19=1919 = 19