Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-3x+3)& = & 14 \color{red}{-} (-2+x) \\\Leftrightarrow & -12x+12& = &14+2-x \\\Leftrightarrow & -12x \color{red}{+12} & = &16 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -12x+x& = &16-12 \\\Leftrightarrow & -11x& = &4 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{4}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-4}{11} & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (2x-3)& = & 13 \color{red}{-} (14+3x) \\\Leftrightarrow & 8x-12& = &13-14-3x \\\Leftrightarrow & 8x \color{red}{-12} & = &-1 \color{red}{-3x} \\\Leftrightarrow & 8x \color{red}{-12} \color{blue}{+12} \color{blue}{+3x} & = &-1 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+12} \\\Leftrightarrow & 8x+3x& = &-1+12 \\\Leftrightarrow & 11x& = &11 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{11}{ \color{red}{11} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-6x+6)& = & 7 \color{red}{-} (9+x) \\\Leftrightarrow & -30x+30& = &7-9-x \\\Leftrightarrow & -30x \color{red}{+30} & = &-2 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & -30x+x& = &-2-30 \\\Leftrightarrow & -29x& = &-32 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-32}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{32}{29} & & \\ & V = \left\{ \frac{32}{29} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-3x+5)& = & 10 \color{red}{-} (14+x) \\\Leftrightarrow & -6x+10& = &10-14-x \\\Leftrightarrow & -6x \color{red}{+10} & = &-4 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & -6x+x& = &-4-10 \\\Leftrightarrow & -5x& = &-14 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-14}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{14}{5} & & \\ & V = \left\{ \frac{14}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-x-4)& = & -1 \color{red}{+} (12-3x) \\\Leftrightarrow & -4x-16& = &-1+12-3x \\\Leftrightarrow & -4x \color{red}{-16} & = &11 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-16} \color{blue}{+16} \color{blue}{+3x} & = &11 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+16} \\\Leftrightarrow & -4x+3x& = &11+16 \\\Leftrightarrow & -x& = &27 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{27}{ \color{red}{-1} } \\\Leftrightarrow & x = -27 & & \\ & V = \left\{ -27 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (6x-1)& = & 8 \color{red}{+} (-4-5x) \\\Leftrightarrow & 36x-6& = &8-4-5x \\\Leftrightarrow & 36x \color{red}{-6} & = &4 \color{red}{-5x} \\\Leftrightarrow & 36x \color{red}{-6} \color{blue}{+6} \color{blue}{+5x} & = &4 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+6} \\\Leftrightarrow & 36x+5x& = &4+6 \\\Leftrightarrow & 41x& = &10 \\\Leftrightarrow & \frac{41x}{ \color{red}{41} }& = &\frac{10}{ \color{red}{41} } \\\Leftrightarrow & x = \frac{10}{41} & & \\ & V = \left\{ \frac{10}{41} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-4x+4)& = & -2 \color{red}{-} (-13+x) \\\Leftrightarrow & -24x+24& = &-2+13-x \\\Leftrightarrow & -24x \color{red}{+24} & = &11 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & -24x+x& = &11-24 \\\Leftrightarrow & -23x& = &-13 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-13}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{13}{23} & & \\ & V = \left\{ \frac{13}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (3x-5)& = & 1 \color{red}{-} (13-5x) \\\Leftrightarrow & 6x-10& = &1-13+5x \\\Leftrightarrow & 6x \color{red}{-10} & = &-12 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{-10} \color{blue}{+10} \color{blue}{-5x} & = &-12 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+10} \\\Leftrightarrow & 6x-5x& = &-12+10 \\\Leftrightarrow & x& = &-2 \\ & V = \left\{ -2 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (2x-4)& = & -15 \color{red}{+} (12-5x) \\\Leftrightarrow & 6x-12& = &-15+12-5x \\\Leftrightarrow & 6x \color{red}{-12} & = &-3 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{-12} \color{blue}{+12} \color{blue}{+5x} & = &-3 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+12} \\\Leftrightarrow & 6x+5x& = &-3+12 \\\Leftrightarrow & 11x& = &9 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{9}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{9}{11} & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (5x-1)& = & -15 \color{red}{-} (-1+x) \\\Leftrightarrow & 10x-2& = &-15+1-x \\\Leftrightarrow & 10x \color{red}{-2} & = &-14 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{-2} \color{blue}{+2} \color{blue}{+x} & = &-14 \color{red}{-x} \color{blue}{+x} \color{blue}{+2} \\\Leftrightarrow & 10x+x& = &-14+2 \\\Leftrightarrow & 11x& = &-12 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-12}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-12}{11} & & \\ & V = \left\{ \frac{-12}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-2x+2)& = & 12 \color{red}{+} (-3+x) \\\Leftrightarrow & -4x+4& = &12-3+x \\\Leftrightarrow & -4x \color{red}{+4} & = &9 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & -4x-x& = &9-4 \\\Leftrightarrow & -5x& = &5 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{5}{ \color{red}{-5} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (x-7)& = & 5 \color{red}{+} (6+x) \\\Leftrightarrow & 6x-42& = &5+6+x \\\Leftrightarrow & 6x \color{red}{-42} & = &11 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & 6x-x& = &11+42 \\\Leftrightarrow & 5x& = &53 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{53}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{53}{5} & & \\ & V = \left\{ \frac{53}{5} \right\} & \\\end{align}\)