Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (3x-3)& = & -14 \color{red}{+} (-9+x) \\\Leftrightarrow & 15x-15& = &-14-9+x \\\Leftrightarrow & 15x \color{red}{-15} & = &-23 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &-23 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & 15x-x& = &-23+15 \\\Leftrightarrow & 14x& = &-8 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{-8}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{-4}{7} & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (5x-5)& = & -4 \color{red}{+} (4-3x) \\\Leftrightarrow & 10x-10& = &-4+4-3x \\\Leftrightarrow & 10x \color{red}{-10} & = &0 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{-10} \color{blue}{+10} \color{blue}{+3x} & = &0 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+10} \\\Leftrightarrow & 10x+3x& = &0+10 \\\Leftrightarrow & 13x& = &10 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{10}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{10}{13} & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (5x+3)& = & 11 \color{red}{+} (-9+x) \\\Leftrightarrow & 25x+15& = &11-9+x \\\Leftrightarrow & 25x \color{red}{+15} & = &2 \color{red}{+x} \\\Leftrightarrow & 25x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & 25x-x& = &2-15 \\\Leftrightarrow & 24x& = &-13 \\\Leftrightarrow & \frac{24x}{ \color{red}{24} }& = &\frac{-13}{ \color{red}{24} } \\\Leftrightarrow & x = \frac{-13}{24} & & \\ & V = \left\{ \frac{-13}{24} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (3x-2)& = & -12 \color{red}{+} (-11+x) \\\Leftrightarrow & 15x-10& = &-12-11+x \\\Leftrightarrow & 15x \color{red}{-10} & = &-23 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &-23 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & 15x-x& = &-23+10 \\\Leftrightarrow & 14x& = &-13 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{-13}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{-13}{14} & & \\ & V = \left\{ \frac{-13}{14} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-4x-3)& = & 13 \color{red}{-} (-3+3x) \\\Leftrightarrow & -8x-6& = &13+3-3x \\\Leftrightarrow & -8x \color{red}{-6} & = &16 \color{red}{-3x} \\\Leftrightarrow & -8x \color{red}{-6} \color{blue}{+6} \color{blue}{+3x} & = &16 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+6} \\\Leftrightarrow & -8x+3x& = &16+6 \\\Leftrightarrow & -5x& = &22 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{22}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-22}{5} & & \\ & V = \left\{ \frac{-22}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-x-6)& = & -1 \color{red}{-} (6+x) \\\Leftrightarrow & -2x-12& = &-1-6-x \\\Leftrightarrow & -2x \color{red}{-12} & = &-7 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -2x+x& = &-7+12 \\\Leftrightarrow & -x& = &5 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{5}{ \color{red}{-1} } \\\Leftrightarrow & x = -5 & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (x-7)& = & -10 \color{red}{-} (-5-2x) \\\Leftrightarrow & 3x-21& = &-10+5+2x \\\Leftrightarrow & 3x \color{red}{-21} & = &-5 \color{red}{+2x} \\\Leftrightarrow & 3x \color{red}{-21} \color{blue}{+21} \color{blue}{-2x} & = &-5 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+21} \\\Leftrightarrow & 3x-2x& = &-5+21 \\\Leftrightarrow & x& = &16 \\ & V = \left\{ 16 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (x+5)& = & 15 \color{red}{+} (-10+4x) \\\Leftrightarrow & 5x+25& = &15-10+4x \\\Leftrightarrow & 5x \color{red}{+25} & = &5 \color{red}{+4x} \\\Leftrightarrow & 5x \color{red}{+25} \color{blue}{-25} \color{blue}{-4x} & = &5 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-25} \\\Leftrightarrow & 5x-4x& = &5-25 \\\Leftrightarrow & x& = &-20 \\ & V = \left\{ -20 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (6x-6)& = & -7 \color{red}{-} (-2-5x) \\\Leftrightarrow & 18x-18& = &-7+2+5x \\\Leftrightarrow & 18x \color{red}{-18} & = &-5 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{-18} \color{blue}{+18} \color{blue}{-5x} & = &-5 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+18} \\\Leftrightarrow & 18x-5x& = &-5+18 \\\Leftrightarrow & 13x& = &13 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{13}{ \color{red}{13} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (5x+7)& = & -6 \color{red}{-} (8+x) \\\Leftrightarrow & 30x+42& = &-6-8-x \\\Leftrightarrow & 30x \color{red}{+42} & = &-14 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &-14 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & 30x+x& = &-14-42 \\\Leftrightarrow & 31x& = &-56 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-56}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-56}{31} & & \\ & V = \left\{ \frac{-56}{31} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-4x-3)& = & 2 \color{red}{-} (-9+x) \\\Leftrightarrow & -24x-18& = &2+9-x \\\Leftrightarrow & -24x \color{red}{-18} & = &11 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & -24x+x& = &11+18 \\\Leftrightarrow & -23x& = &29 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{29}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-29}{23} & & \\ & V = \left\{ \frac{-29}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-6x+4)& = & -7 \color{red}{+} (-6+x) \\\Leftrightarrow & -18x+12& = &-7-6+x \\\Leftrightarrow & -18x \color{red}{+12} & = &-13 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-13 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -18x-x& = &-13-12 \\\Leftrightarrow & -19x& = &-25 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-25}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{25}{19} & & \\ & V = \left\{ \frac{25}{19} \right\} & \\\end{align}\)