Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (3x+2)& = & 10 \color{red}{+} (2+x) \\\Leftrightarrow & 18x+12& = &10+2+x \\\Leftrightarrow & 18x \color{red}{+12} & = &12 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 18x-x& = &12-12 \\\Leftrightarrow & 17x& = &0 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{0}{ \color{red}{17} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-x-2)& = & -6 \color{red}{-} (5+4x) \\\Leftrightarrow & -3x-6& = &-6-5-4x \\\Leftrightarrow & -3x \color{red}{-6} & = &-11 \color{red}{-4x} \\\Leftrightarrow & -3x \color{red}{-6} \color{blue}{+6} \color{blue}{+4x} & = &-11 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+6} \\\Leftrightarrow & -3x+4x& = &-11+6 \\\Leftrightarrow & x& = &-5 \\ & V = \left\{ -5 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (x+7)& = & 4 \color{red}{-} (-8-3x) \\\Leftrightarrow & 4x+28& = &4+8+3x \\\Leftrightarrow & 4x \color{red}{+28} & = &12 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+28} \color{blue}{-28} \color{blue}{-3x} & = &12 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-28} \\\Leftrightarrow & 4x-3x& = &12-28 \\\Leftrightarrow & x& = &-16 \\ & V = \left\{ -16 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-5x+1)& = & -10 \color{red}{+} (2+x) \\\Leftrightarrow & -30x+6& = &-10+2+x \\\Leftrightarrow & -30x \color{red}{+6} & = &-8 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -30x-x& = &-8-6 \\\Leftrightarrow & -31x& = &-14 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-14}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{14}{31} & & \\ & V = \left\{ \frac{14}{31} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (5x+6)& = & 10 \color{red}{-} (-1+x) \\\Leftrightarrow & 20x+24& = &10+1-x \\\Leftrightarrow & 20x \color{red}{+24} & = &11 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 20x+x& = &11-24 \\\Leftrightarrow & 21x& = &-13 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-13}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-13}{21} & & \\ & V = \left\{ \frac{-13}{21} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-6x-4)& = & 10 \color{red}{-} (-5+x) \\\Leftrightarrow & -36x-24& = &10+5-x \\\Leftrightarrow & -36x \color{red}{-24} & = &15 \color{red}{-x} \\\Leftrightarrow & -36x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &15 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -36x+x& = &15+24 \\\Leftrightarrow & -35x& = &39 \\\Leftrightarrow & \frac{-35x}{ \color{red}{-35} }& = &\frac{39}{ \color{red}{-35} } \\\Leftrightarrow & x = \frac{-39}{35} & & \\ & V = \left\{ \frac{-39}{35} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-x-6)& = & -15 \color{red}{-} (-7+x) \\\Leftrightarrow & -3x-18& = &-15+7-x \\\Leftrightarrow & -3x \color{red}{-18} & = &-8 \color{red}{-x} \\\Leftrightarrow & -3x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & -3x+x& = &-8+18 \\\Leftrightarrow & -2x& = &10 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{10}{ \color{red}{-2} } \\\Leftrightarrow & x = -5 & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-3x-7)& = & -3 \color{red}{-} (-13+x) \\\Leftrightarrow & -12x-28& = &-3+13-x \\\Leftrightarrow & -12x \color{red}{-28} & = &10 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-28} \color{blue}{+28} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{+28} \\\Leftrightarrow & -12x+x& = &10+28 \\\Leftrightarrow & -11x& = &38 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{38}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-38}{11} & & \\ & V = \left\{ \frac{-38}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-6x-6)& = & -10 \color{red}{-} (5+x) \\\Leftrightarrow & -24x-24& = &-10-5-x \\\Leftrightarrow & -24x \color{red}{-24} & = &-15 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-15 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -24x+x& = &-15+24 \\\Leftrightarrow & -23x& = &9 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{9}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-9}{23} & & \\ & V = \left\{ \frac{-9}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-5x+2)& = & -2 \color{red}{+} (10-2x) \\\Leftrightarrow & -15x+6& = &-2+10-2x \\\Leftrightarrow & -15x \color{red}{+6} & = &8 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{+6} \color{blue}{-6} \color{blue}{+2x} & = &8 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-6} \\\Leftrightarrow & -15x+2x& = &8-6 \\\Leftrightarrow & -13x& = &2 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{2}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-2}{13} & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-6x+5)& = & -5 \color{red}{-} (-8+x) \\\Leftrightarrow & -18x+15& = &-5+8-x \\\Leftrightarrow & -18x \color{red}{+15} & = &3 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & -18x+x& = &3-15 \\\Leftrightarrow & -17x& = &-12 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-12}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{12}{17} & & \\ & V = \left\{ \frac{12}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (x-7)& = & -3 \color{red}{-} (-7+3x) \\\Leftrightarrow & 2x-14& = &-3+7-3x \\\Leftrightarrow & 2x \color{red}{-14} & = &4 \color{red}{-3x} \\\Leftrightarrow & 2x \color{red}{-14} \color{blue}{+14} \color{blue}{+3x} & = &4 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+14} \\\Leftrightarrow & 2x+3x& = &4+14 \\\Leftrightarrow & 5x& = &18 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{18}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{18}{5} & & \\ & V = \left\{ \frac{18}{5} \right\} & \\\end{align}\)