Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (6x+5)& = & 3 \color{red}{+} (-14+x) \\\Leftrightarrow & 12x+10& = &3-14+x \\\Leftrightarrow & 12x \color{red}{+10} & = &-11 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & 12x-x& = &-11-10 \\\Leftrightarrow & 11x& = &-21 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-21}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-21}{11} & & \\ & V = \left\{ \frac{-21}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (3x-6)& = & 13 \color{red}{+} (-6+x) \\\Leftrightarrow & 18x-36& = &13-6+x \\\Leftrightarrow & 18x \color{red}{-36} & = &7 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-36} \color{blue}{+36} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{+36} \\\Leftrightarrow & 18x-x& = &7+36 \\\Leftrightarrow & 17x& = &43 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{43}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{43}{17} & & \\ & V = \left\{ \frac{43}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (6x-2)& = & 14 \color{red}{-} (-9+x) \\\Leftrightarrow & 30x-10& = &14+9-x \\\Leftrightarrow & 30x \color{red}{-10} & = &23 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &23 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & 30x+x& = &23+10 \\\Leftrightarrow & 31x& = &33 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{33}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{33}{31} & & \\ & V = \left\{ \frac{33}{31} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-x+2)& = & -13 \color{red}{+} (8+x) \\\Leftrightarrow & -6x+12& = &-13+8+x \\\Leftrightarrow & -6x \color{red}{+12} & = &-5 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -6x-x& = &-5-12 \\\Leftrightarrow & -7x& = &-17 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-17}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{17}{7} & & \\ & V = \left\{ \frac{17}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-3x+3)& = & -1 \color{red}{-} (8+x) \\\Leftrightarrow & -12x+12& = &-1-8-x \\\Leftrightarrow & -12x \color{red}{+12} & = &-9 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -12x+x& = &-9-12 \\\Leftrightarrow & -11x& = &-21 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-21}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{21}{11} & & \\ & V = \left\{ \frac{21}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-x-6)& = & -12 \color{red}{-} (-3+x) \\\Leftrightarrow & -2x-12& = &-12+3-x \\\Leftrightarrow & -2x \color{red}{-12} & = &-9 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -2x+x& = &-9+12 \\\Leftrightarrow & -x& = &3 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{3}{ \color{red}{-1} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (x-3)& = & 3 \color{red}{+} (8-2x) \\\Leftrightarrow & 3x-9& = &3+8-2x \\\Leftrightarrow & 3x \color{red}{-9} & = &11 \color{red}{-2x} \\\Leftrightarrow & 3x \color{red}{-9} \color{blue}{+9} \color{blue}{+2x} & = &11 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+9} \\\Leftrightarrow & 3x+2x& = &11+9 \\\Leftrightarrow & 5x& = &20 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{20}{ \color{red}{5} } \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-3x-2)& = & 8 \color{red}{+} (-10-2x) \\\Leftrightarrow & -15x-10& = &8-10-2x \\\Leftrightarrow & -15x \color{red}{-10} & = &-2 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{-10} \color{blue}{+10} \color{blue}{+2x} & = &-2 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+10} \\\Leftrightarrow & -15x+2x& = &-2+10 \\\Leftrightarrow & -13x& = &8 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{8}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-8}{13} & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-4x-1)& = & 13 \color{red}{-} (1+x) \\\Leftrightarrow & -8x-2& = &13-1-x \\\Leftrightarrow & -8x \color{red}{-2} & = &12 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{-2} \color{blue}{+2} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{+2} \\\Leftrightarrow & -8x+x& = &12+2 \\\Leftrightarrow & -7x& = &14 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{14}{ \color{red}{-7} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-4x+5)& = & 10 \color{red}{+} (-14+x) \\\Leftrightarrow & -12x+15& = &10-14+x \\\Leftrightarrow & -12x \color{red}{+15} & = &-4 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & -12x-x& = &-4-15 \\\Leftrightarrow & -13x& = &-19 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-19}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{19}{13} & & \\ & V = \left\{ \frac{19}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-5x+4)& = & -6 \color{red}{+} (-9-2x) \\\Leftrightarrow & -15x+12& = &-6-9-2x \\\Leftrightarrow & -15x \color{red}{+12} & = &-15 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{+12} \color{blue}{-12} \color{blue}{+2x} & = &-15 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-12} \\\Leftrightarrow & -15x+2x& = &-15-12 \\\Leftrightarrow & -13x& = &-27 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-27}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{27}{13} & & \\ & V = \left\{ \frac{27}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-3x+1)& = & -1 \color{red}{+} (8-5x) \\\Leftrightarrow & -18x+6& = &-1+8-5x \\\Leftrightarrow & -18x \color{red}{+6} & = &7 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{+6} \color{blue}{-6} \color{blue}{+5x} & = &7 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-6} \\\Leftrightarrow & -18x+5x& = &7-6 \\\Leftrightarrow & -13x& = &1 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{1}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-1}{13} & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)