Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (x-7)& = & 3 \color{red}{+} (-3+x) \\\Leftrightarrow & 3x-21& = &3-3+x \\\Leftrightarrow & 3x \color{red}{-21} & = &0 \color{red}{+x} \\\Leftrightarrow & 3x \color{red}{-21} \color{blue}{+21} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+21} \\\Leftrightarrow & 3x-x& = &0+21 \\\Leftrightarrow & 2x& = &21 \\\Leftrightarrow & \frac{2x}{ \color{red}{2} }& = &\frac{21}{ \color{red}{2} } \\\Leftrightarrow & x = \frac{21}{2} & & \\ & V = \left\{ \frac{21}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (x+2)& = & 15 \color{red}{-} (1+x) \\\Leftrightarrow & 5x+10& = &15-1-x \\\Leftrightarrow & 5x \color{red}{+10} & = &14 \color{red}{-x} \\\Leftrightarrow & 5x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & 5x+x& = &14-10 \\\Leftrightarrow & 6x& = &4 \\\Leftrightarrow & \frac{6x}{ \color{red}{6} }& = &\frac{4}{ \color{red}{6} } \\\Leftrightarrow & x = \frac{2}{3} & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (2x+3)& = & -9 \color{red}{-} (-13-3x) \\\Leftrightarrow & 4x+6& = &-9+13+3x \\\Leftrightarrow & 4x \color{red}{+6} & = &4 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+6} \color{blue}{-6} \color{blue}{-3x} & = &4 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-6} \\\Leftrightarrow & 4x-3x& = &4-6 \\\Leftrightarrow & x& = &-2 \\ & V = \left\{ -2 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-2x+3)& = & 7 \color{red}{+} (-5+x) \\\Leftrightarrow & -6x+9& = &7-5+x \\\Leftrightarrow & -6x \color{red}{+9} & = &2 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+9} \color{blue}{-9} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-9} \\\Leftrightarrow & -6x-x& = &2-9 \\\Leftrightarrow & -7x& = &-7 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-7}{ \color{red}{-7} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (x+7)& = & 10 \color{red}{+} (12+x) \\\Leftrightarrow & 4x+28& = &10+12+x \\\Leftrightarrow & 4x \color{red}{+28} & = &22 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &22 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & 4x-x& = &22-28 \\\Leftrightarrow & 3x& = &-6 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-6}{ \color{red}{3} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (3x-1)& = & -4 \color{red}{-} (-13+2x) \\\Leftrightarrow & 9x-3& = &-4+13-2x \\\Leftrightarrow & 9x \color{red}{-3} & = &9 \color{red}{-2x} \\\Leftrightarrow & 9x \color{red}{-3} \color{blue}{+3} \color{blue}{+2x} & = &9 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+3} \\\Leftrightarrow & 9x+2x& = &9+3 \\\Leftrightarrow & 11x& = &12 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{12}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{12}{11} & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-6x-1)& = & 8 \color{red}{+} (-14-5x) \\\Leftrightarrow & -36x-6& = &8-14-5x \\\Leftrightarrow & -36x \color{red}{-6} & = &-6 \color{red}{-5x} \\\Leftrightarrow & -36x \color{red}{-6} \color{blue}{+6} \color{blue}{+5x} & = &-6 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+6} \\\Leftrightarrow & -36x+5x& = &-6+6 \\\Leftrightarrow & -31x& = &0 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{0}{ \color{red}{-31} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-3x-3)& = & -15 \color{red}{+} (4+x) \\\Leftrightarrow & -6x-6& = &-15+4+x \\\Leftrightarrow & -6x \color{red}{-6} & = &-11 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -6x-x& = &-11+6 \\\Leftrightarrow & -7x& = &-5 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-5}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{5}{7} & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-5x+2)& = & -11 \color{red}{-} (-9-4x) \\\Leftrightarrow & -25x+10& = &-11+9+4x \\\Leftrightarrow & -25x \color{red}{+10} & = &-2 \color{red}{+4x} \\\Leftrightarrow & -25x \color{red}{+10} \color{blue}{-10} \color{blue}{-4x} & = &-2 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-10} \\\Leftrightarrow & -25x-4x& = &-2-10 \\\Leftrightarrow & -29x& = &-12 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-12}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{12}{29} & & \\ & V = \left\{ \frac{12}{29} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (x+1)& = & -14 \color{red}{-} (-9+x) \\\Leftrightarrow & 6x+6& = &-14+9-x \\\Leftrightarrow & 6x \color{red}{+6} & = &-5 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 6x+x& = &-5-6 \\\Leftrightarrow & 7x& = &-11 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-11}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-11}{7} & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (4x-7)& = & -2 \color{red}{-} (-8+x) \\\Leftrightarrow & 8x-14& = &-2+8-x \\\Leftrightarrow & 8x \color{red}{-14} & = &6 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{-14} \color{blue}{+14} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{+14} \\\Leftrightarrow & 8x+x& = &6+14 \\\Leftrightarrow & 9x& = &20 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{20}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{20}{9} & & \\ & V = \left\{ \frac{20}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (6x-2)& = & 3 \color{red}{-} (9+x) \\\Leftrightarrow & 30x-10& = &3-9-x \\\Leftrightarrow & 30x \color{red}{-10} & = &-6 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & 30x+x& = &-6+10 \\\Leftrightarrow & 31x& = &4 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{4}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{4}{31} & & \\ & V = \left\{ \frac{4}{31} \right\} & \\\end{align}\)