Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(3(-2x-5)=9+(-14+x)\)
2. \(3(-x+7)=7+(-4-2x)\)
3. \(6(4x-1)=3-(7+x)\)
4. \(2(-6x+5)=-1-(10+x)\)
5. \(4(-2x-5)=13-(-4+3x)\)
6. \(4(-x-5)=-4+(1+x)\)
7. \(5(-x-4)=-4+(5+x)\)
8. \(3(-5x-7)=-9-(-13+4x)\)
9. \(2(-x+5)=-11-(13+x)\)
10. \(2(5x-2)=-15-(-1-3x)\)
11. \(2(-2x-3)=7-(-2+x)\)
12. \(6(6x+2)=-8+(-6+x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-2x-5)& = & 9 \color{red}{+} (-14+x) \\\Leftrightarrow & -6x-15& = &9-14+x \\\Leftrightarrow & -6x \color{red}{-15} & = &-5 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & -6x-x& = &-5+15 \\\Leftrightarrow & -7x& = &10 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{10}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-10}{7} & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-x+7)& = & 7 \color{red}{+} (-4-2x) \\\Leftrightarrow & -3x+21& = &7-4-2x \\\Leftrightarrow & -3x \color{red}{+21} & = &3 \color{red}{-2x} \\\Leftrightarrow & -3x \color{red}{+21} \color{blue}{-21} \color{blue}{+2x} & = &3 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-21} \\\Leftrightarrow & -3x+2x& = &3-21 \\\Leftrightarrow & -x& = &-18 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-18}{ \color{red}{-1} } \\\Leftrightarrow & x = 18 & & \\ & V = \left\{ 18 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (4x-1)& = & 3 \color{red}{-} (7+x) \\\Leftrightarrow & 24x-6& = &3-7-x \\\Leftrightarrow & 24x \color{red}{-6} & = &-4 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 24x+x& = &-4+6 \\\Leftrightarrow & 25x& = &2 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{2}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{2}{25} & & \\ & V = \left\{ \frac{2}{25} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-6x+5)& = & -1 \color{red}{-} (10+x) \\\Leftrightarrow & -12x+10& = &-1-10-x \\\Leftrightarrow & -12x \color{red}{+10} & = &-11 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & -12x+x& = &-11-10 \\\Leftrightarrow & -11x& = &-21 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-21}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{21}{11} & & \\ & V = \left\{ \frac{21}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-2x-5)& = & 13 \color{red}{-} (-4+3x) \\\Leftrightarrow & -8x-20& = &13+4-3x \\\Leftrightarrow & -8x \color{red}{-20} & = &17 \color{red}{-3x} \\\Leftrightarrow & -8x \color{red}{-20} \color{blue}{+20} \color{blue}{+3x} & = &17 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+20} \\\Leftrightarrow & -8x+3x& = &17+20 \\\Leftrightarrow & -5x& = &37 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{37}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-37}{5} & & \\ & V = \left\{ \frac{-37}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-x-5)& = & -4 \color{red}{+} (1+x) \\\Leftrightarrow & -4x-20& = &-4+1+x \\\Leftrightarrow & -4x \color{red}{-20} & = &-3 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & -4x-x& = &-3+20 \\\Leftrightarrow & -5x& = &17 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{17}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-17}{5} & & \\ & V = \left\{ \frac{-17}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-x-4)& = & -4 \color{red}{+} (5+x) \\\Leftrightarrow & -5x-20& = &-4+5+x \\\Leftrightarrow & -5x \color{red}{-20} & = &1 \color{red}{+x} \\\Leftrightarrow & -5x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & -5x-x& = &1+20 \\\Leftrightarrow & -6x& = &21 \\\Leftrightarrow & \frac{-6x}{ \color{red}{-6} }& = &\frac{21}{ \color{red}{-6} } \\\Leftrightarrow & x = \frac{-7}{2} & & \\ & V = \left\{ \frac{-7}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-5x-7)& = & -9 \color{red}{-} (-13+4x) \\\Leftrightarrow & -15x-21& = &-9+13-4x \\\Leftrightarrow & -15x \color{red}{-21} & = &4 \color{red}{-4x} \\\Leftrightarrow & -15x \color{red}{-21} \color{blue}{+21} \color{blue}{+4x} & = &4 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+21} \\\Leftrightarrow & -15x+4x& = &4+21 \\\Leftrightarrow & -11x& = &25 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{25}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-25}{11} & & \\ & V = \left\{ \frac{-25}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-x+5)& = & -11 \color{red}{-} (13+x) \\\Leftrightarrow & -2x+10& = &-11-13-x \\\Leftrightarrow & -2x \color{red}{+10} & = &-24 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &-24 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & -2x+x& = &-24-10 \\\Leftrightarrow & -x& = &-34 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-34}{ \color{red}{-1} } \\\Leftrightarrow & x = 34 & & \\ & V = \left\{ 34 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (5x-2)& = & -15 \color{red}{-} (-1-3x) \\\Leftrightarrow & 10x-4& = &-15+1+3x \\\Leftrightarrow & 10x \color{red}{-4} & = &-14 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{-4} \color{blue}{+4} \color{blue}{-3x} & = &-14 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+4} \\\Leftrightarrow & 10x-3x& = &-14+4 \\\Leftrightarrow & 7x& = &-10 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-10}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-10}{7} & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-2x-3)& = & 7 \color{red}{-} (-2+x) \\\Leftrightarrow & -4x-6& = &7+2-x \\\Leftrightarrow & -4x \color{red}{-6} & = &9 \color{red}{-x} \\\Leftrightarrow & -4x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -4x+x& = &9+6 \\\Leftrightarrow & -3x& = &15 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{15}{ \color{red}{-3} } \\\Leftrightarrow & x = -5 & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (6x+2)& = & -8 \color{red}{+} (-6+x) \\\Leftrightarrow & 36x+12& = &-8-6+x \\\Leftrightarrow & 36x \color{red}{+12} & = &-14 \color{red}{+x} \\\Leftrightarrow & 36x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 36x-x& = &-14-12 \\\Leftrightarrow & 35x& = &-26 \\\Leftrightarrow & \frac{35x}{ \color{red}{35} }& = &\frac{-26}{ \color{red}{35} } \\\Leftrightarrow & x = \frac{-26}{35} & & \\ & V = \left\{ \frac{-26}{35} \right\} & \\\end{align}\)