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  1. Asked: November 27, 2020In:

    Solve for x in the inequality \dfrac{1}{x+1}> -\dfrac{1}{3}

    Sengemegz
    Sengemegz Moderator

    $\dfrac{1}{x+1}> -\dfrac{1}{3}$ cross multiply $1\times 3> -1(x+1)$ $\Rightarrow 3> -x-1$ collect like terms $x> -1-3$ $\Rightarrow x> -4$

    \dfrac{1}{x+1}> -\dfrac{1}{3}
    cross multiply
    1\times 3> -1(x+1)
    \Rightarrow 3> -x-1
    collect like terms
    x> -1-3
    \Rightarrow x> -4

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  2. Asked: November 27, 2020In:

    Solve for x in the inequality 7-3(x-1)< 13

    Sengemegz
    Sengemegz Moderator

    $7-3(x-1)< 13$ open up the bracket $7-3x+3< 13$ collect like terms $-3x< 13-7-3$ $\Rightarrow -3x \dfrac{3}{-3}$ $\therefore x> -1$

    7-3(x-1)< 13
    open up the bracket
    7-3x+3< 13
    collect like terms
    -3x< 13-7-3
    \Rightarrow -3x \dfrac{3}{-3}
    \therefore x> -1

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  3. Asked: November 27, 2020In:

    Solve for y in the inequality 12\geq 3(2y-3)

    Sengemegz
    Sengemegz Moderator

    $12\geq 3(2y-3)$ open up the bracket $12\geq 6y-9$ add 9 to both sides $12+9\geq 6y$ $\Rightarrow 21\geq 6y$ divide both sides by 6 $\therefore \dfrac{21}{6}\geq y$ $y\leq \dfrac{7}{2}$

    12\geq 3(2y-3)
    open up the bracket
    12\geq 6y-9
    add 9 to both sides
    12+9\geq 6y
    \Rightarrow 21\geq 6y
    divide both sides by 6
    \therefore \dfrac{21}{6}\geq y
    y\leq \dfrac{7}{2}

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  4. Asked: November 27, 2020In:

    Solve for x in the inequality \dfrac{x}{3}+2> x-2

    Sengemegz
    Sengemegz Moderator

    $\dfrac{x}{3}+2> x-2$ multiply through by the LCM (3) $3\times \dfrac{x}{3}+3\times 2> 3\times x-3\times2$ $\Rightarrow x+6> 3x-6$ collect like terms $x-3x>-6-6$ $\Rightarrow -2x> -12$ divide both side by -2 $\therefore x<6$

    \dfrac{x}{3}+2> x-2
    multiply through by the LCM (3)
    3\times \dfrac{x}{3}+3\times 2> 3\times x-3\times2
    \Rightarrow x+6> 3x-6
    collect like terms
    x-3x>-6-6
    \Rightarrow -2x> -12
    divide both side by -2
    \therefore x<6

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  5. Asked: November 27, 2020In:

    Solve for x in the inequality \dfrac{x}{4}-\dfrac{3x}{5}\geq 3-\dfrac{x}{2}

    Sengemegz
    Sengemegz Moderator

    $\dfrac{x}{4}-\dfrac{3x}{5}\geq 3-\dfrac{x}{2}$ multiply through by the LCM (20) $20\times \dfrac{x}{4}-20\times \dfrac{3x}{5}\geq 20\times 3-20\times \dfrac{x}{2}$ $\Rightarrow 5x-12x\geq 60-10x$ collect like terms $5x-12x+10x\geq 60$ $\Rightarrow 3x\geq 60$ divide both side by 3 $\therefore x\geqRead more

    \dfrac{x}{4}-\dfrac{3x}{5}\geq 3-\dfrac{x}{2}
    multiply through by the LCM (20)
    20\times \dfrac{x}{4}-20\times \dfrac{3x}{5}\geq 20\times 3-20\times \dfrac{x}{2}
    \Rightarrow 5x-12x\geq 60-10x
    collect like terms
    5x-12x+10x\geq 60
    \Rightarrow 3x\geq 60
    divide both side by 3
    \therefore x\geq 20

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  6. Asked: November 27, 2020In:

    Solve for x in the inequality \dfrac{-5}{2}\geq 3x

    Sengemegz
    Sengemegz Moderator

    $\dfrac{-5}{2}\geq 3x$ cross multiply $-5\leq 2\times 3x$ $\Rightarrow -5\geq 6x$ divide both sides by 6 $\therefore \dfrac{-5}{6}\geq x$ $x\leq \dfrac{-5}{6}$

    \dfrac{-5}{2}\geq 3x
    cross multiply
    -5\leq 2\times 3x
    \Rightarrow -5\geq 6x
    divide both sides by 6
    \therefore \dfrac{-5}{6}\geq x
    x\leq \dfrac{-5}{6}

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  7. Asked: November 27, 2020In:

    Solve for x in the inequality \dfrac{-4}{3}\geq 2x

    Sengemegz
    Sengemegz Moderator

    $\dfrac{-4}{3}\geq 2x$ cross multiply $-4\leq 3\times 2x$ $\Rightarrow -4\geq 6x$ divide both sides by 6 $\therefore \dfrac{-4}{6}\geq x$ $x\leq \dfrac{-2}{3}$

    \dfrac{-4}{3}\geq 2x
    cross multiply
    -4\leq 3\times 2x
    \Rightarrow -4\geq 6x
    divide both sides by 6
    \therefore \dfrac{-4}{6}\geq x
    x\leq \dfrac{-2}{3}

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  8. Asked: November 27, 2020In:

    What is the value of y in \dfrac{y+3}{y-1}\leq 2 ?

    Sengemegz
    Sengemegz Moderator

    $\dfrac{y+3}{y-1}\leq2$ cross multiply $y+3\leq 2(y-1)$ open up the bracket $y+3\leq 2y-2$ collect like terms $y-2y\leq -2-3$ $\Rightarrow -y\leq -5$ divide both sides by -1 $ \therefore y\geq 5$

    \dfrac{y+3}{y-1}\leq2
    cross multiply
    y+3\leq 2(y-1)
    open up the bracket
    y+3\leq 2y-2
    collect like terms
    y-2y\leq -2-3
    \Rightarrow -y\leq -5
    divide both sides by -1
    \therefore y\geq 5

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  9. Asked: November 27, 2020In:

    Find the value of \sin 420^{0}

    Sengemegz
    Sengemegz Moderator

    $\sin 420^{0}$ first step is to subtract 360 from the value above $\cos (420^{0}-360^{0})= \cos 60^{0}$ 60 falls in the first quadrant and sine is positive, using table $\therefore \sin 60^{0}=0.866$

    \sin 420^{0}
    first step is to subtract 360 from the value above
    \cos (420^{0}-360^{0})= \cos 60^{0}
    60 falls in the first quadrant and sine is positive,
    using table
    \therefore \sin 60^{0}=0.866

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  10. Asked: November 27, 2020In:

    Find the value of \cos 690^{0}

    Sengemegz
    Sengemegz Moderator

    $\cos 690^{0}$ first step is to subtract 360 from the value above $\cos (690^{0}-360^{0})= \cos 330^{0}$ 330 falls in the fourth quadrant and cosine is positive $\Rightarrow +\cos (360^{0}-330^{0})=\cos 30^{0}$ using table $\therefore \cos 30^{0}=0.866$

    \cos 690^{0}
    first step is to subtract 360 from the value above
    \cos (690^{0}-360^{0})= \cos 330^{0}
    330 falls in the fourth quadrant and cosine is positive
    \Rightarrow +\cos (360^{0}-330^{0})=\cos 30^{0}
    using table
    \therefore \cos 30^{0}=0.866

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