Solve the first part of the inequality: 4 - 3x < x + 12.

Step 1: Solve the first part of the inequality: 4 - 3x < x + 12. 4 - 3x < x + 12 Subtract x from both sides: 4 - 4x < 12 Subtract 4 from both sides: -4x < 8 Divide by -4. Remember to reverse the inequality sign when dividing by a negative number: x > (8)/(-4) x > -2 Step 2: Solve the second part of the inequality: x + 12 (-3x + 29)/(2). x + 12 (-3x + 29)/(2) Multiply both sides by 2: 2(x + 12) -3x + 29 2x + 24 -3x + 29 Add 3x to both sides: 5x + 24 29 Subtract 24 from both sides: 5x 5 Divide by 5: x 1 Step 3: Combine the solutions. We have x > -2 and x 1. This can be written as: -2 < x 1 Step 4: Illustrate the solution on a number line. The solution includes all numbers greater than -2 and less than or equal to 1. On a number line, this is represented by an open circle at -2 (since -2 is not included), a closed circle at 1 (since 1 is included), and a line segment connecting these two points. ` <-----|-----|-----|-----|-----|-----|-----|-----> -3 -2 -1 0 1 2 3 o------------------• ` The solution is -2 < x 1. Step 1: Evaluate each term in the expression. ((1)/(27))^(1)/(3) = ((1)/(3^3))^(1)/(3) = (3^-3)^(1)/(3) = 3^-3 × (1)/(3) = 3^-1 = (1)/(3) sqrt(256 × 9) = sqrt(256) × sqrt(9) = 16 × 3 = 48 729^-1 = (1)/(729) 72^2 = (8 × 9)^2 = 8^2 × 9^2 = 64 × 81 Step 2: Substitute the evaluated terms back into the expression. (1)/(3) × 48(1)/(729) × 72^2 Step 3: Simplify the numerator. (1)/(3) × 48 = 16 Step 4: Simplify the denominator. (1)/(729) × 72^2 = (1)/(9^3) × (8 × 9)^2 = (1)/(9^3) × 8^2 × 9^2 = (8^2)/(9) = (64)/(9) Step 5: Divide the simplified numerator by the simplified denominator. (16)/(64)9 = 16 × (9)/(64) = (16 × 9)/(64) = (1 × 9)/(4) = (9)/(4) The evaluated expression is (9)/(4). Step 1: Calculate the amount in Kenya Shillings (Ksh) the tourist received from changing South African Rands (SAR). On 12/1/2024, the tourist sells SAR to the bank, so the bank buys SAR. Buying rate for 1 SAR = 7.08 Ksh. Amount in Ksh = 15\,000 SAR × 7.08 Ksh/SAR = 106\,200 Ksh. Step 2: Calculate the remaining Kenya Shillings after spending. Amount spent = 53 075 Ksh. Remaining Ksh = 106\,200 Ksh - 53\,075 Ksh = 53\,125 Ksh. Step 3: Calculate the amount in Tanzanian Shillings (Tsh) the tourist received from changing the remaining Kenya Shillings. On 12/2/2024, the tourist buys Tsh from the bank, so the bank sells Tsh. Selling rate for 100 Tanzanian Shillings = 21.25 Ksh. This means 1 Tsh = (21.25)/(100) Ksh = 0.2125 Ksh. Amount in Tsh = Remaining KshKsh per Tsh Amount in Tsh = 53\,125 Ksh0.2125 Ksh/Tsh = 250\,000 Tsh. The amount received in Tanzanian shillings is 250\,000 Tsh. That's 2 down. 3 left today — send the next one.