Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-5x+7)& = & 2 \color{red}{-} (-8+3x) \\\Leftrightarrow & -20x+28& = &2+8-3x \\\Leftrightarrow & -20x \color{red}{+28} & = &10 \color{red}{-3x} \\\Leftrightarrow & -20x \color{red}{+28} \color{blue}{-28} \color{blue}{+3x} & = &10 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-28} \\\Leftrightarrow & -20x+3x& = &10-28 \\\Leftrightarrow & -17x& = &-18 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-18}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{18}{17} & & \\ & V = \left\{ \frac{18}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (x-5)& = & -8 \color{red}{-} (-6+x) \\\Leftrightarrow & 6x-30& = &-8+6-x \\\Leftrightarrow & 6x \color{red}{-30} & = &-2 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 6x+x& = &-2+30 \\\Leftrightarrow & 7x& = &28 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{28}{ \color{red}{7} } \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (6x-4)& = & -7 \color{red}{+} (3-5x) \\\Leftrightarrow & 18x-12& = &-7+3-5x \\\Leftrightarrow & 18x \color{red}{-12} & = &-4 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{-12} \color{blue}{+12} \color{blue}{+5x} & = &-4 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+12} \\\Leftrightarrow & 18x+5x& = &-4+12 \\\Leftrightarrow & 23x& = &8 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{8}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{8}{23} & & \\ & V = \left\{ \frac{8}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-5x-1)& = & 4 \color{red}{-} (-12+x) \\\Leftrightarrow & -15x-3& = &4+12-x \\\Leftrightarrow & -15x \color{red}{-3} & = &16 \color{red}{-x} \\\Leftrightarrow & -15x \color{red}{-3} \color{blue}{+3} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{+3} \\\Leftrightarrow & -15x+x& = &16+3 \\\Leftrightarrow & -14x& = &19 \\\Leftrightarrow & \frac{-14x}{ \color{red}{-14} }& = &\frac{19}{ \color{red}{-14} } \\\Leftrightarrow & x = \frac{-19}{14} & & \\ & V = \left\{ \frac{-19}{14} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-3x-7)& = & -13 \color{red}{-} (6+x) \\\Leftrightarrow & -9x-21& = &-13-6-x \\\Leftrightarrow & -9x \color{red}{-21} & = &-19 \color{red}{-x} \\\Leftrightarrow & -9x \color{red}{-21} \color{blue}{+21} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{+21} \\\Leftrightarrow & -9x+x& = &-19+21 \\\Leftrightarrow & -8x& = &2 \\\Leftrightarrow & \frac{-8x}{ \color{red}{-8} }& = &\frac{2}{ \color{red}{-8} } \\\Leftrightarrow & x = \frac{-1}{4} & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-x+5)& = & -14 \color{red}{-} (1+3x) \\\Leftrightarrow & -4x+20& = &-14-1-3x \\\Leftrightarrow & -4x \color{red}{+20} & = &-15 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+20} \color{blue}{-20} \color{blue}{+3x} & = &-15 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-20} \\\Leftrightarrow & -4x+3x& = &-15-20 \\\Leftrightarrow & -x& = &-35 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-35}{ \color{red}{-1} } \\\Leftrightarrow & x = 35 & & \\ & V = \left\{ 35 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (x+1)& = & 14 \color{red}{-} (6+x) \\\Leftrightarrow & 5x+5& = &14-6-x \\\Leftrightarrow & 5x \color{red}{+5} & = &8 \color{red}{-x} \\\Leftrightarrow & 5x \color{red}{+5} \color{blue}{-5} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{-5} \\\Leftrightarrow & 5x+x& = &8-5 \\\Leftrightarrow & 6x& = &3 \\\Leftrightarrow & \frac{6x}{ \color{red}{6} }& = &\frac{3}{ \color{red}{6} } \\\Leftrightarrow & x = \frac{1}{2} & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (x+6)& = & -13 \color{red}{+} (10+x) \\\Leftrightarrow & 3x+18& = &-13+10+x \\\Leftrightarrow & 3x \color{red}{+18} & = &-3 \color{red}{+x} \\\Leftrightarrow & 3x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & 3x-x& = &-3-18 \\\Leftrightarrow & 2x& = &-21 \\\Leftrightarrow & \frac{2x}{ \color{red}{2} }& = &\frac{-21}{ \color{red}{2} } \\\Leftrightarrow & x = \frac{-21}{2} & & \\ & V = \left\{ \frac{-21}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (5x-2)& = & 11 \color{red}{-} (2+x) \\\Leftrightarrow & 30x-12& = &11-2-x \\\Leftrightarrow & 30x \color{red}{-12} & = &9 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 30x+x& = &9+12 \\\Leftrightarrow & 31x& = &21 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{21}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{21}{31} & & \\ & V = \left\{ \frac{21}{31} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-4x-6)& = & -15 \color{red}{-} (9-5x) \\\Leftrightarrow & -8x-12& = &-15-9+5x \\\Leftrightarrow & -8x \color{red}{-12} & = &-24 \color{red}{+5x} \\\Leftrightarrow & -8x \color{red}{-12} \color{blue}{+12} \color{blue}{-5x} & = &-24 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+12} \\\Leftrightarrow & -8x-5x& = &-24+12 \\\Leftrightarrow & -13x& = &-12 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-12}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{12}{13} & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (3x-7)& = & 8 \color{red}{+} (13+x) \\\Leftrightarrow & 6x-14& = &8+13+x \\\Leftrightarrow & 6x \color{red}{-14} & = &21 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-14} \color{blue}{+14} \color{blue}{-x} & = &21 \color{red}{+x} \color{blue}{-x} \color{blue}{+14} \\\Leftrightarrow & 6x-x& = &21+14 \\\Leftrightarrow & 5x& = &35 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{35}{ \color{red}{5} } \\\Leftrightarrow & x = 7 & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-2x-6)& = & 11 \color{red}{+} (14-3x) \\\Leftrightarrow & -4x-12& = &11+14-3x \\\Leftrightarrow & -4x \color{red}{-12} & = &25 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-12} \color{blue}{+12} \color{blue}{+3x} & = &25 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+12} \\\Leftrightarrow & -4x+3x& = &25+12 \\\Leftrightarrow & -x& = &37 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{37}{ \color{red}{-1} } \\\Leftrightarrow & x = -37 & & \\ & V = \left\{ -37 \right\} & \\\end{align}\)