Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (4x-6)& = & -14 \color{red}{-} (-8-3x) \\\Leftrightarrow & 16x-24& = &-14+8+3x \\\Leftrightarrow & 16x \color{red}{-24} & = &-6 \color{red}{+3x} \\\Leftrightarrow & 16x \color{red}{-24} \color{blue}{+24} \color{blue}{-3x} & = &-6 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+24} \\\Leftrightarrow & 16x-3x& = &-6+24 \\\Leftrightarrow & 13x& = &18 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{18}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{18}{13} & & \\ & V = \left\{ \frac{18}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (6x+2)& = & 2 \color{red}{+} (-8+x) \\\Leftrightarrow & 12x+4& = &2-8+x \\\Leftrightarrow & 12x \color{red}{+4} & = &-6 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & 12x-x& = &-6-4 \\\Leftrightarrow & 11x& = &-10 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-10}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-10}{11} & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (4x-5)& = & 15 \color{red}{-} (-3+x) \\\Leftrightarrow & 20x-25& = &15+3-x \\\Leftrightarrow & 20x \color{red}{-25} & = &18 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-25} \color{blue}{+25} \color{blue}{+x} & = &18 \color{red}{-x} \color{blue}{+x} \color{blue}{+25} \\\Leftrightarrow & 20x+x& = &18+25 \\\Leftrightarrow & 21x& = &43 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{43}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{43}{21} & & \\ & V = \left\{ \frac{43}{21} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (3x+1)& = & 8 \color{red}{+} (-1-4x) \\\Leftrightarrow & 9x+3& = &8-1-4x \\\Leftrightarrow & 9x \color{red}{+3} & = &7 \color{red}{-4x} \\\Leftrightarrow & 9x \color{red}{+3} \color{blue}{-3} \color{blue}{+4x} & = &7 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-3} \\\Leftrightarrow & 9x+4x& = &7-3 \\\Leftrightarrow & 13x& = &4 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{4}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{4}{13} & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-3x+7)& = & 6 \color{red}{+} (-8+x) \\\Leftrightarrow & -15x+35& = &6-8+x \\\Leftrightarrow & -15x \color{red}{+35} & = &-2 \color{red}{+x} \\\Leftrightarrow & -15x \color{red}{+35} \color{blue}{-35} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{-35} \\\Leftrightarrow & -15x-x& = &-2-35 \\\Leftrightarrow & -16x& = &-37 \\\Leftrightarrow & \frac{-16x}{ \color{red}{-16} }& = &\frac{-37}{ \color{red}{-16} } \\\Leftrightarrow & x = \frac{37}{16} & & \\ & V = \left\{ \frac{37}{16} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-x-7)& = & 12 \color{red}{-} (14+4x) \\\Leftrightarrow & -3x-21& = &12-14-4x \\\Leftrightarrow & -3x \color{red}{-21} & = &-2 \color{red}{-4x} \\\Leftrightarrow & -3x \color{red}{-21} \color{blue}{+21} \color{blue}{+4x} & = &-2 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+21} \\\Leftrightarrow & -3x+4x& = &-2+21 \\\Leftrightarrow & x& = &19 \\ & V = \left\{ 19 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (4x-5)& = & -5 \color{red}{+} (15+x) \\\Leftrightarrow & 12x-15& = &-5+15+x \\\Leftrightarrow & 12x \color{red}{-15} & = &10 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & 12x-x& = &10+15 \\\Leftrightarrow & 11x& = &25 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{25}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{25}{11} & & \\ & V = \left\{ \frac{25}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (2x+1)& = & 13 \color{red}{-} (3-5x) \\\Leftrightarrow & 8x+4& = &13-3+5x \\\Leftrightarrow & 8x \color{red}{+4} & = &10 \color{red}{+5x} \\\Leftrightarrow & 8x \color{red}{+4} \color{blue}{-4} \color{blue}{-5x} & = &10 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-4} \\\Leftrightarrow & 8x-5x& = &10-4 \\\Leftrightarrow & 3x& = &6 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{6}{ \color{red}{3} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-4x-5)& = & -8 \color{red}{+} (-9-5x) \\\Leftrightarrow & -16x-20& = &-8-9-5x \\\Leftrightarrow & -16x \color{red}{-20} & = &-17 \color{red}{-5x} \\\Leftrightarrow & -16x \color{red}{-20} \color{blue}{+20} \color{blue}{+5x} & = &-17 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+20} \\\Leftrightarrow & -16x+5x& = &-17+20 \\\Leftrightarrow & -11x& = &3 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{3}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-3}{11} & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (x-5)& = & 15 \color{red}{-} (-8+x) \\\Leftrightarrow & 2x-10& = &15+8-x \\\Leftrightarrow & 2x \color{red}{-10} & = &23 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &23 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & 2x+x& = &23+10 \\\Leftrightarrow & 3x& = &33 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{33}{ \color{red}{3} } \\\Leftrightarrow & x = 11 & & \\ & V = \left\{ 11 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (4x+4)& = & 3 \color{red}{-} (11+x) \\\Leftrightarrow & 8x+8& = &3-11-x \\\Leftrightarrow & 8x \color{red}{+8} & = &-8 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & 8x+x& = &-8-8 \\\Leftrightarrow & 9x& = &-16 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-16}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-16}{9} & & \\ & V = \left\{ \frac{-16}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-6x+7)& = & -5 \color{red}{-} (-15+x) \\\Leftrightarrow & -24x+28& = &-5+15-x \\\Leftrightarrow & -24x \color{red}{+28} & = &10 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+28} \color{blue}{-28} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{-28} \\\Leftrightarrow & -24x+x& = &10-28 \\\Leftrightarrow & -23x& = &-18 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-18}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{18}{23} & & \\ & V = \left\{ \frac{18}{23} \right\} & \\\end{align}\)