Solve the inequality below and write down the integral values that satisfy the equality

Here's the solution for questions 9 and 10: 9. Solve the inequality below and write down the integral values that satisfy the equality -3x + 2 < x + 6 17 - 2x Step 1: Split the compound inequality into two separate inequalities. -3x + 2 < x + 6 and x + 6 17 - 2x Step 2: Solve the first inequality. -3x + 2 &< x + 6 \\ -3x - x &< 6 - 2 \\ -4x &< 4 Divide by -4 and reverse the inequality sign: x > (4)/(-4) \\ x > -1 Step 3: Solve the second inequality. x + 6 & 17 - 2x \\ x + 2x & 17 - 6 \\ 3x & 11 Divide by 3: x (11)/(3) Step 4: Combine the solutions and identify the integral values. The combined inequality is -1 < x (11)/(3). Since (11)/(3) ≈ 3.67, the integral values (integers) that satisfy this condition are those greater than -1 and less than or equal to 3.67. The integral values are 0, 1, 2, 3. 10. Find the equation of a line which passes through the point (2, 3) and is perpendicular to y - 3x + 1 = 0, giving your answer in the form y = mx + c. Step 1: Find the slope of the given line. The given equation is y - 3x + 1 = 0. Rearrange it into the form y = mx + c: y = 3x - 1 The slope of this line, m_1, is 3. Step 2: Find the slope of the perpendicular line. For two lines to be perpendicular, the product of their slopes must be -1. Let m_2 be the slope of the required line. m_1 · m_2 = -1 \\ 3 · m_2 = -1 \\ m_2 = -(1)/(3) Step 3: Use the point-slope form to find the equation of the required line. The line passes through (x_1, y_1) = (2, 3) and has a slope m_2 = -(1)/(3). The point-slope form is y - y_1 = m(x - x_1). y - 3 = -(1)/(3)(x - 2) Step 4: Convert the equation to the y = mx + c form. y - 3 = -(1)/(3)x + (2)/(3) \\ y = -(1)/(3)x + (2)/(3) + 3 \\ y = -(1)/(3)x + (2)/(3) + (9)/(3) \\ y = -(1)/(3)x + (11)/(3) The equation of the line is y = -(1)/(3)x + (11)/(3). Last free one today — make it count tomorrow, or type /upgrade for unlimited.