Solve the following algebraic equations for the unknown variable: 1. 2 - x + 1 = 8x 2. 2x - 8 + 3x = 17 3. (2)/(5)y + 8 = 12 4. Thrice a number divided by 2 results in 10 less than the number.

Here are the solutions to the problems: 1. Find the unknown variable in the following equation: 2 - x + 1 = 8x. Step 1: Combine the constant terms on the left side. 3 - x = 8x Step 2: Add x to both sides of the equation. 3 = 8x + x 3 = 9x Step 3: Divide both sides by 9 to solve for x. x = (3)/(9) x = (1)/(3) The unknown variable is (1)/(3). 2. Find the unknown variable in the following equation: 2x - 8 + 3x = 17. Step 1: Combine the like terms on the left side of the equation. (2x + 3x) - 8 = 17 5x - 8 = 17 Step 2: Add 8 to both sides of the equation. 5x = 17 + 8 5x = 25 Step 3: Divide both sides by 5 to solve for x. x = (25)/(5) x = 5 The unknown variable is 5. 3. Find the unknown variable in the following equation: (2)/(5)y + 8 = 12. Step 1: Subtract 8 from both sides of the equation. (2)/(5)y = 12 - 8 (2)/(5)y = 4 Step 2: Multiply both sides by the reciprocal of (2)/(5), which is (5)/(2). y = 4 × (5)/(2) y = (20)/(2) y = 10 The unknown variable is 10. 4. Thrice a number divided by 2 results in 10 less than the number. What is the number? Step 1: Let the number be n. Translate the problem into an equation. (3n)/(2) = n - 10 Step 2: Multiply both sides by 2 to eliminate the fraction. 3n = 2(n - 10) 3n = 2n - 20 Step 3: Subtract 2n from both sides of the equation. 3n - 2n = -20 n = -20 The number is -20. 5. The product of a number and five is increased by 12, and the result is 32. Find the number. Step 1: Let the number be x. Translate the problem into an equation. 5x + 12 = 32 Step 2: Subtract 12 from both sides of the equation. 5x = 32 - 12 5x = 20 Step 3: Divide both sides by 5 to solve for x. x = (20)/(5) x = 4 The number is 4. Send me the next one 📸