Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (3x+3)& = & 12 \color{red}{-} (13+x) \\\Leftrightarrow & 18x+18& = &12-13-x \\\Leftrightarrow & 18x \color{red}{+18} & = &-1 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 18x+x& = &-1-18 \\\Leftrightarrow & 19x& = &-19 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-19}{ \color{red}{19} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (2x+3)& = & -9 \color{red}{+} (-2+x) \\\Leftrightarrow & 12x+18& = &-9-2+x \\\Leftrightarrow & 12x \color{red}{+18} & = &-11 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & 12x-x& = &-11-18 \\\Leftrightarrow & 11x& = &-29 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-29}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-29}{11} & & \\ & V = \left\{ \frac{-29}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-2x-4)& = & -12 \color{red}{+} (-13+3x) \\\Leftrightarrow & -4x-8& = &-12-13+3x \\\Leftrightarrow & -4x \color{red}{-8} & = &-25 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-8} \color{blue}{+8} \color{blue}{-3x} & = &-25 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+8} \\\Leftrightarrow & -4x-3x& = &-25+8 \\\Leftrightarrow & -7x& = &-17 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-17}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{17}{7} & & \\ & V = \left\{ \frac{17}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (4x+2)& = & 1 \color{red}{-} (3+x) \\\Leftrightarrow & 20x+10& = &1-3-x \\\Leftrightarrow & 20x \color{red}{+10} & = &-2 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & 20x+x& = &-2-10 \\\Leftrightarrow & 21x& = &-12 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-12}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-4}{7} & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (3x-1)& = & -5 \color{red}{-} (-3-5x) \\\Leftrightarrow & 18x-6& = &-5+3+5x \\\Leftrightarrow & 18x \color{red}{-6} & = &-2 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{-6} \color{blue}{+6} \color{blue}{-5x} & = &-2 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+6} \\\Leftrightarrow & 18x-5x& = &-2+6 \\\Leftrightarrow & 13x& = &4 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{4}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{4}{13} & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (2x+7)& = & 1 \color{red}{-} (7+x) \\\Leftrightarrow & 12x+42& = &1-7-x \\\Leftrightarrow & 12x \color{red}{+42} & = &-6 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & 12x+x& = &-6-42 \\\Leftrightarrow & 13x& = &-48 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-48}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-48}{13} & & \\ & V = \left\{ \frac{-48}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-3x-4)& = & 4 \color{red}{+} (2-5x) \\\Leftrightarrow & -6x-8& = &4+2-5x \\\Leftrightarrow & -6x \color{red}{-8} & = &6 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-8} \color{blue}{+8} \color{blue}{+5x} & = &6 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+8} \\\Leftrightarrow & -6x+5x& = &6+8 \\\Leftrightarrow & -x& = &14 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{14}{ \color{red}{-1} } \\\Leftrightarrow & x = -14 & & \\ & V = \left\{ -14 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-5x-4)& = & -10 \color{red}{+} (8-4x) \\\Leftrightarrow & -25x-20& = &-10+8-4x \\\Leftrightarrow & -25x \color{red}{-20} & = &-2 \color{red}{-4x} \\\Leftrightarrow & -25x \color{red}{-20} \color{blue}{+20} \color{blue}{+4x} & = &-2 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+20} \\\Leftrightarrow & -25x+4x& = &-2+20 \\\Leftrightarrow & -21x& = &18 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{18}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-6}{7} & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (6x-7)& = & 6 \color{red}{+} (10+x) \\\Leftrightarrow & 12x-14& = &6+10+x \\\Leftrightarrow & 12x \color{red}{-14} & = &16 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-14} \color{blue}{+14} \color{blue}{-x} & = &16 \color{red}{+x} \color{blue}{-x} \color{blue}{+14} \\\Leftrightarrow & 12x-x& = &16+14 \\\Leftrightarrow & 11x& = &30 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{30}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{30}{11} & & \\ & V = \left\{ \frac{30}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-4x-5)& = & -12 \color{red}{-} (9+x) \\\Leftrightarrow & -12x-15& = &-12-9-x \\\Leftrightarrow & -12x \color{red}{-15} & = &-21 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &-21 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & -12x+x& = &-21+15 \\\Leftrightarrow & -11x& = &-6 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-6}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{6}{11} & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-6x-2)& = & 4 \color{red}{+} (15+x) \\\Leftrightarrow & -24x-8& = &4+15+x \\\Leftrightarrow & -24x \color{red}{-8} & = &19 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &19 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & -24x-x& = &19+8 \\\Leftrightarrow & -25x& = &27 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{27}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-27}{25} & & \\ & V = \left\{ \frac{-27}{25} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-6x-1)& = & -3 \color{red}{+} (1+x) \\\Leftrightarrow & -30x-5& = &-3+1+x \\\Leftrightarrow & -30x \color{red}{-5} & = &-2 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-5} \color{blue}{+5} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{+5} \\\Leftrightarrow & -30x-x& = &-2+5 \\\Leftrightarrow & -31x& = &3 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{3}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-3}{31} & & \\ & V = \left\{ \frac{-3}{31} \right\} & \\\end{align}\)