Mathematics

Question

Mathematics MH helpo
Mathematics MH helpo

2 Answer

  • The inequalities that require flipping the sign are:

    -5x - 10 > 5

    [tex]\frac{x}{-7} + 3 \leq 4[/tex]

    Solution:

    Let us the inequalities one by one

    You can perform on operations on both sides of inequality, and have its truth value unchanged

    But if we multiply or divide by a negative number , we must flip the sign

    option 1)

    -5x - 10 > 5

    Move -10 from L.H.S to R.H.S

    -5x > 5 + 10

    -5x > 15

    Divide the above expression by 5

    [tex]-x > 3[/tex]

    Divide the above inequality by -1, so we must flip the sign

    x < -3

    option 2)

    [tex]7x - 5 \leq 16[/tex]

    Move the constant term from L.H.S to R.H.S

    [tex]7x \leq 16 + 5\\\\7x \leq 21\\\\[/tex]

    Divide the above inequality by 7

    [tex]x \leq 3[/tex]

    This does not required flipping the symbol

    option 3

    [tex]\frac{x}{5} - 6 > -11[/tex]

    Move the constant term from L.H.S to R.H.S

    [tex]\frac{x}{5} > -11 + 6\\\\\frac{x}{5} > -5[/tex]

    Multiply both the sides by 5

    [tex]x > -25[/tex]

    This does not required flipping the symbol

    option 4

    [tex]x + 12 \leq 29[/tex]

    Move the constant term from L.H.S to R.H.S

    [tex]x \leq 29 - 12\\\\x \leq 17[/tex]

    This does not required flipping the symbol

    option 5

    [tex]\frac{x}{-7} + 3 \leq 4[/tex]

    Move the constant term from L.H.S to R.H.S

    [tex]\frac{x}{-7} \leq 4-3\\\\\frac{x}{-7} \leq 1\\\\[/tex]

    Multiply both the sides by -7, so we must flip the sign

    [tex]x \geq -7[/tex]

    Thus this requires flipping the sign

  • Answer: -5x - 10 > 5

    Step-by-step explanation: