This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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You're on a roll — here are the solutions to the problems from the image: 1. 2(2a-3) = 5(4+x) This equation contains two variables, a and x. From a single equation, we can express one variable in terms of the other, but we cannot find a unique numerical value for either a or x. Step 1: Distribute the constants on both sides of the equation. 2(2a) - 2(3) = 5(4) + 5(x) 4a - 6 = 20 + 5x Step 2: Isolate a by adding 6 to both sides. 4a = 20 + 5x + 6 4a = 26 + 5x Step 3: Divide by 4 to express a in terms of x. a = (26 + 5x)/(4) a = (26 + 5x)/(4) (Alternatively, we could express x in terms of a: 5x = 4a - 26 x = (4a - 26)/(5)) 2. 3(5a-3) = 4(2a+9) Step 1: Distribute the constants on both sides of the equation. 3(5a) - 3(3) = 4(2a) + 4(9) 15a - 9 = 8a + 36 Step 2: Subtract 8a from both sides of the equation. 15a - 8a - 9 = 36 7a - 9 = 36 Step 3: Add 9 to both sides of the equation. 7a = 36 + 9 7a = 45 Step 4: Divide both sides by 7 to solve for a. a = (45)/(7) a = (45)/(7) 3. 5x - (x-10) = 0 Step 1: Distribute the negative sign into the parentheses. 5x - x + 10 = 0 Step 2: Combine like terms. 4x + 10 = 0 Step 3: Subtract 10 from both sides of the equation. 4x = -10 Step 4: Divide both sides by 4 to solve for x. x = (-10)/(4) x = -(5)/(2) x = -(5)/(2) 4. 9 - (2x-1) = -12 Step 1: Distribute the negative sign into the parentheses. 9 - 2x + 1 = -12 Step 2: Combine the constant terms on the left side. 10 - 2x = -12 Step 3: Subtract 10 from both sides of the equation. -2x = -12 - 10 -2x = -22 Step 4: Divide both sides by -2 to solve for x. x = (-22)/(-2) x = 11 x = 11 Got more? Send 'em!