Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (3x+5)& = & 12 \color{red}{-} (-6+x) \\\Leftrightarrow & 9x+15& = &12+6-x \\\Leftrightarrow & 9x \color{red}{+15} & = &18 \color{red}{-x} \\\Leftrightarrow & 9x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &18 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & 9x+x& = &18-15 \\\Leftrightarrow & 10x& = &3 \\\Leftrightarrow & \frac{10x}{ \color{red}{10} }& = &\frac{3}{ \color{red}{10} } \\\Leftrightarrow & x = \frac{3}{10} & & \\ & V = \left\{ \frac{3}{10} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-6x-7)& = & -5 \color{red}{-} (7+x) \\\Leftrightarrow & -18x-21& = &-5-7-x \\\Leftrightarrow & -18x \color{red}{-21} & = &-12 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{-21} \color{blue}{+21} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{+21} \\\Leftrightarrow & -18x+x& = &-12+21 \\\Leftrightarrow & -17x& = &9 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{9}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-9}{17} & & \\ & V = \left\{ \frac{-9}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-4x-3)& = & 13 \color{red}{+} (2+x) \\\Leftrightarrow & -24x-18& = &13+2+x \\\Leftrightarrow & -24x \color{red}{-18} & = &15 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & -24x-x& = &15+18 \\\Leftrightarrow & -25x& = &33 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{33}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-33}{25} & & \\ & V = \left\{ \frac{-33}{25} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-3x-7)& = & 10 \color{red}{-} (10+x) \\\Leftrightarrow & -12x-28& = &10-10-x \\\Leftrightarrow & -12x \color{red}{-28} & = &0 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-28} \color{blue}{+28} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+28} \\\Leftrightarrow & -12x+x& = &0+28 \\\Leftrightarrow & -11x& = &28 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{28}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-28}{11} & & \\ & V = \left\{ \frac{-28}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-x+7)& = & -9 \color{red}{+} (14+x) \\\Leftrightarrow & -5x+35& = &-9+14+x \\\Leftrightarrow & -5x \color{red}{+35} & = &5 \color{red}{+x} \\\Leftrightarrow & -5x \color{red}{+35} \color{blue}{-35} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{-35} \\\Leftrightarrow & -5x-x& = &5-35 \\\Leftrightarrow & -6x& = &-30 \\\Leftrightarrow & \frac{-6x}{ \color{red}{-6} }& = &\frac{-30}{ \color{red}{-6} } \\\Leftrightarrow & x = 5 & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-3x+3)& = & -11 \color{red}{-} (13+x) \\\Leftrightarrow & -15x+15& = &-11-13-x \\\Leftrightarrow & -15x \color{red}{+15} & = &-24 \color{red}{-x} \\\Leftrightarrow & -15x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &-24 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & -15x+x& = &-24-15 \\\Leftrightarrow & -14x& = &-39 \\\Leftrightarrow & \frac{-14x}{ \color{red}{-14} }& = &\frac{-39}{ \color{red}{-14} } \\\Leftrightarrow & x = \frac{39}{14} & & \\ & V = \left\{ \frac{39}{14} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (6x+6)& = & -12 \color{red}{+} (12+x) \\\Leftrightarrow & 24x+24& = &-12+12+x \\\Leftrightarrow & 24x \color{red}{+24} & = &0 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 24x-x& = &0-24 \\\Leftrightarrow & 23x& = &-24 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-24}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-24}{23} & & \\ & V = \left\{ \frac{-24}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (6x+6)& = & 4 \color{red}{+} (-11+x) \\\Leftrightarrow & 18x+18& = &4-11+x \\\Leftrightarrow & 18x \color{red}{+18} & = &-7 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & 18x-x& = &-7-18 \\\Leftrightarrow & 17x& = &-25 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-25}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-25}{17} & & \\ & V = \left\{ \frac{-25}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-x-7)& = & 12 \color{red}{+} (2+x) \\\Leftrightarrow & -6x-42& = &12+2+x \\\Leftrightarrow & -6x \color{red}{-42} & = &14 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &14 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & -6x-x& = &14+42 \\\Leftrightarrow & -7x& = &56 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{56}{ \color{red}{-7} } \\\Leftrightarrow & x = -8 & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-6x+1)& = & -9 \color{red}{+} (-2+x) \\\Leftrightarrow & -12x+2& = &-9-2+x \\\Leftrightarrow & -12x \color{red}{+2} & = &-11 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+2} \color{blue}{-2} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{-2} \\\Leftrightarrow & -12x-x& = &-11-2 \\\Leftrightarrow & -13x& = &-13 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-13}{ \color{red}{-13} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-4x-6)& = & -6 \color{red}{-} (4+x) \\\Leftrightarrow & -16x-24& = &-6-4-x \\\Leftrightarrow & -16x \color{red}{-24} & = &-10 \color{red}{-x} \\\Leftrightarrow & -16x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -16x+x& = &-10+24 \\\Leftrightarrow & -15x& = &14 \\\Leftrightarrow & \frac{-15x}{ \color{red}{-15} }& = &\frac{14}{ \color{red}{-15} } \\\Leftrightarrow & x = \frac{-14}{15} & & \\ & V = \left\{ \frac{-14}{15} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (4x+2)& = & -15 \color{red}{-} (4+x) \\\Leftrightarrow & 8x+4& = &-15-4-x \\\Leftrightarrow & 8x \color{red}{+4} & = &-19 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 8x+x& = &-19-4 \\\Leftrightarrow & 9x& = &-23 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-23}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-23}{9} & & \\ & V = \left\{ \frac{-23}{9} \right\} & \\\end{align}\)