Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (3x+1)& = & 9 \color{red}{-} (-14-5x) \\\Leftrightarrow & 6x+2& = &9+14+5x \\\Leftrightarrow & 6x \color{red}{+2} & = &23 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+2} \color{blue}{-2} \color{blue}{-5x} & = &23 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-2} \\\Leftrightarrow & 6x-5x& = &23-2 \\\Leftrightarrow & x& = &21 \\ & V = \left\{ 21 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (6x-5)& = & -1 \color{red}{+} (11+x) \\\Leftrightarrow & 24x-20& = &-1+11+x \\\Leftrightarrow & 24x \color{red}{-20} & = &10 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & 24x-x& = &10+20 \\\Leftrightarrow & 23x& = &30 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{30}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{30}{23} & & \\ & V = \left\{ \frac{30}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (6x+7)& = & -15 \color{red}{-} (-8+x) \\\Leftrightarrow & 30x+35& = &-15+8-x \\\Leftrightarrow & 30x \color{red}{+35} & = &-7 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+35} \color{blue}{-35} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{-35} \\\Leftrightarrow & 30x+x& = &-7-35 \\\Leftrightarrow & 31x& = &-42 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-42}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-42}{31} & & \\ & V = \left\{ \frac{-42}{31} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (x+5)& = & -10 \color{red}{+} (-1+3x) \\\Leftrightarrow & 2x+10& = &-10-1+3x \\\Leftrightarrow & 2x \color{red}{+10} & = &-11 \color{red}{+3x} \\\Leftrightarrow & 2x \color{red}{+10} \color{blue}{-10} \color{blue}{-3x} & = &-11 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-10} \\\Leftrightarrow & 2x-3x& = &-11-10 \\\Leftrightarrow & -x& = &-21 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-21}{ \color{red}{-1} } \\\Leftrightarrow & x = 21 & & \\ & V = \left\{ 21 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-2x-4)& = & -14 \color{red}{+} (14-5x) \\\Leftrightarrow & -6x-12& = &-14+14-5x \\\Leftrightarrow & -6x \color{red}{-12} & = &0 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-12} \color{blue}{+12} \color{blue}{+5x} & = &0 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+12} \\\Leftrightarrow & -6x+5x& = &0+12 \\\Leftrightarrow & -x& = &12 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{12}{ \color{red}{-1} } \\\Leftrightarrow & x = -12 & & \\ & V = \left\{ -12 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-3x+3)& = & -13 \color{red}{+} (13+x) \\\Leftrightarrow & -6x+6& = &-13+13+x \\\Leftrightarrow & -6x \color{red}{+6} & = &0 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -6x-x& = &0-6 \\\Leftrightarrow & -7x& = &-6 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-6}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{6}{7} & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (2x+4)& = & -6 \color{red}{-} (-4-3x) \\\Leftrightarrow & 4x+8& = &-6+4+3x \\\Leftrightarrow & 4x \color{red}{+8} & = &-2 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+8} \color{blue}{-8} \color{blue}{-3x} & = &-2 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-8} \\\Leftrightarrow & 4x-3x& = &-2-8 \\\Leftrightarrow & x& = &-10 \\ & V = \left\{ -10 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-3x-6)& = & -6 \color{red}{+} (15-2x) \\\Leftrightarrow & -9x-18& = &-6+15-2x \\\Leftrightarrow & -9x \color{red}{-18} & = &9 \color{red}{-2x} \\\Leftrightarrow & -9x \color{red}{-18} \color{blue}{+18} \color{blue}{+2x} & = &9 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+18} \\\Leftrightarrow & -9x+2x& = &9+18 \\\Leftrightarrow & -7x& = &27 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{27}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-27}{7} & & \\ & V = \left\{ \frac{-27}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-4x+3)& = & -9 \color{red}{-} (12+x) \\\Leftrightarrow & -24x+18& = &-9-12-x \\\Leftrightarrow & -24x \color{red}{+18} & = &-21 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &-21 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & -24x+x& = &-21-18 \\\Leftrightarrow & -23x& = &-39 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-39}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{39}{23} & & \\ & V = \left\{ \frac{39}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-6x-7)& = & 9 \color{red}{+} (5+x) \\\Leftrightarrow & -36x-42& = &9+5+x \\\Leftrightarrow & -36x \color{red}{-42} & = &14 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &14 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & -36x-x& = &14+42 \\\Leftrightarrow & -37x& = &56 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{56}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{-56}{37} & & \\ & V = \left\{ \frac{-56}{37} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-2x-3)& = & -5 \color{red}{+} (-3+x) \\\Leftrightarrow & -12x-18& = &-5-3+x \\\Leftrightarrow & -12x \color{red}{-18} & = &-8 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & -12x-x& = &-8+18 \\\Leftrightarrow & -13x& = &10 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{10}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-10}{13} & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (x-1)& = & -14 \color{red}{+} (-6-2x) \\\Leftrightarrow & 3x-3& = &-14-6-2x \\\Leftrightarrow & 3x \color{red}{-3} & = &-20 \color{red}{-2x} \\\Leftrightarrow & 3x \color{red}{-3} \color{blue}{+3} \color{blue}{+2x} & = &-20 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+3} \\\Leftrightarrow & 3x+2x& = &-20+3 \\\Leftrightarrow & 5x& = &-17 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-17}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-17}{5} & & \\ & V = \left\{ \frac{-17}{5} \right\} & \\\end{align}\)