Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-5x+3)& = & 7 \color{red}{-} (-10+x) \\\Leftrightarrow & -30x+18& = &7+10-x \\\Leftrightarrow & -30x \color{red}{+18} & = &17 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &17 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & -30x+x& = &17-18 \\\Leftrightarrow & -29x& = &-1 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-1}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{1}{29} & & \\ & V = \left\{ \frac{1}{29} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (x-1)& = & -7 \color{red}{-} (-12-2x) \\\Leftrightarrow & 5x-5& = &-7+12+2x \\\Leftrightarrow & 5x \color{red}{-5} & = &5 \color{red}{+2x} \\\Leftrightarrow & 5x \color{red}{-5} \color{blue}{+5} \color{blue}{-2x} & = &5 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+5} \\\Leftrightarrow & 5x-2x& = &5+5 \\\Leftrightarrow & 3x& = &10 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{10}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{10}{3} & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (3x-7)& = & -1 \color{red}{-} (3+x) \\\Leftrightarrow & 12x-28& = &-1-3-x \\\Leftrightarrow & 12x \color{red}{-28} & = &-4 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-28} \color{blue}{+28} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{+28} \\\Leftrightarrow & 12x+x& = &-4+28 \\\Leftrightarrow & 13x& = &24 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{24}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{24}{13} & & \\ & V = \left\{ \frac{24}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (5x+1)& = & 15 \color{red}{-} (15+3x) \\\Leftrightarrow & 10x+2& = &15-15-3x \\\Leftrightarrow & 10x \color{red}{+2} & = &0 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+2} \color{blue}{-2} \color{blue}{+3x} & = &0 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-2} \\\Leftrightarrow & 10x+3x& = &0-2 \\\Leftrightarrow & 13x& = &-2 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-2}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-2}{13} & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (5x-3)& = & 8 \color{red}{+} (-9+2x) \\\Leftrightarrow & 25x-15& = &8-9+2x \\\Leftrightarrow & 25x \color{red}{-15} & = &-1 \color{red}{+2x} \\\Leftrightarrow & 25x \color{red}{-15} \color{blue}{+15} \color{blue}{-2x} & = &-1 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+15} \\\Leftrightarrow & 25x-2x& = &-1+15 \\\Leftrightarrow & 23x& = &14 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{14}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{14}{23} & & \\ & V = \left\{ \frac{14}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (3x-3)& = & -11 \color{red}{-} (-14-2x) \\\Leftrightarrow & 15x-15& = &-11+14+2x \\\Leftrightarrow & 15x \color{red}{-15} & = &3 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{-15} \color{blue}{+15} \color{blue}{-2x} & = &3 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+15} \\\Leftrightarrow & 15x-2x& = &3+15 \\\Leftrightarrow & 13x& = &18 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{18}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{18}{13} & & \\ & V = \left\{ \frac{18}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (x-3)& = & 10 \color{red}{+} (3-2x) \\\Leftrightarrow & 3x-9& = &10+3-2x \\\Leftrightarrow & 3x \color{red}{-9} & = &13 \color{red}{-2x} \\\Leftrightarrow & 3x \color{red}{-9} \color{blue}{+9} \color{blue}{+2x} & = &13 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+9} \\\Leftrightarrow & 3x+2x& = &13+9 \\\Leftrightarrow & 5x& = &22 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{22}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{22}{5} & & \\ & V = \left\{ \frac{22}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-4x+1)& = & 9 \color{red}{+} (-10+3x) \\\Leftrightarrow & -8x+2& = &9-10+3x \\\Leftrightarrow & -8x \color{red}{+2} & = &-1 \color{red}{+3x} \\\Leftrightarrow & -8x \color{red}{+2} \color{blue}{-2} \color{blue}{-3x} & = &-1 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-2} \\\Leftrightarrow & -8x-3x& = &-1-2 \\\Leftrightarrow & -11x& = &-3 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-3}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{3}{11} & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (4x-7)& = & -11 \color{red}{-} (12+x) \\\Leftrightarrow & 20x-35& = &-11-12-x \\\Leftrightarrow & 20x \color{red}{-35} & = &-23 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-35} \color{blue}{+35} \color{blue}{+x} & = &-23 \color{red}{-x} \color{blue}{+x} \color{blue}{+35} \\\Leftrightarrow & 20x+x& = &-23+35 \\\Leftrightarrow & 21x& = &12 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{12}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{4}{7} & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-4x+4)& = & -12 \color{red}{+} (3+x) \\\Leftrightarrow & -24x+24& = &-12+3+x \\\Leftrightarrow & -24x \color{red}{+24} & = &-9 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & -24x-x& = &-9-24 \\\Leftrightarrow & -25x& = &-33 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-33}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{33}{25} & & \\ & V = \left\{ \frac{33}{25} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (3x+7)& = & 6 \color{red}{-} (-12+x) \\\Leftrightarrow & 12x+28& = &6+12-x \\\Leftrightarrow & 12x \color{red}{+28} & = &18 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+28} \color{blue}{-28} \color{blue}{+x} & = &18 \color{red}{-x} \color{blue}{+x} \color{blue}{-28} \\\Leftrightarrow & 12x+x& = &18-28 \\\Leftrightarrow & 13x& = &-10 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-10}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-10}{13} & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-x+7)& = & 7 \color{red}{+} (-9+x) \\\Leftrightarrow & -2x+14& = &7-9+x \\\Leftrightarrow & -2x \color{red}{+14} & = &-2 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{+14} \color{blue}{-14} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{-14} \\\Leftrightarrow & -2x-x& = &-2-14 \\\Leftrightarrow & -3x& = &-16 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-16}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{16}{3} & & \\ & V = \left\{ \frac{16}{3} \right\} & \\\end{align}\)