Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (2x+7)& = & 14 \color{red}{+} (-6+3x) \\\Leftrightarrow & 10x+35& = &14-6+3x \\\Leftrightarrow & 10x \color{red}{+35} & = &8 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+35} \color{blue}{-35} \color{blue}{-3x} & = &8 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-35} \\\Leftrightarrow & 10x-3x& = &8-35 \\\Leftrightarrow & 7x& = &-27 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-27}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-27}{7} & & \\ & V = \left\{ \frac{-27}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (2x+3)& = & -7 \color{red}{-} (-5+x) \\\Leftrightarrow & 4x+6& = &-7+5-x \\\Leftrightarrow & 4x \color{red}{+6} & = &-2 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 4x+x& = &-2-6 \\\Leftrightarrow & 5x& = &-8 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-8}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-8}{5} & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (4x-3)& = & -6 \color{red}{+} (7-5x) \\\Leftrightarrow & 16x-12& = &-6+7-5x \\\Leftrightarrow & 16x \color{red}{-12} & = &1 \color{red}{-5x} \\\Leftrightarrow & 16x \color{red}{-12} \color{blue}{+12} \color{blue}{+5x} & = &1 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+12} \\\Leftrightarrow & 16x+5x& = &1+12 \\\Leftrightarrow & 21x& = &13 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{13}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{13}{21} & & \\ & V = \left\{ \frac{13}{21} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (3x+5)& = & 11 \color{red}{+} (-5-2x) \\\Leftrightarrow & 9x+15& = &11-5-2x \\\Leftrightarrow & 9x \color{red}{+15} & = &6 \color{red}{-2x} \\\Leftrightarrow & 9x \color{red}{+15} \color{blue}{-15} \color{blue}{+2x} & = &6 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-15} \\\Leftrightarrow & 9x+2x& = &6-15 \\\Leftrightarrow & 11x& = &-9 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-9}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-9}{11} & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-5x-2)& = & -8 \color{red}{-} (14+x) \\\Leftrightarrow & -20x-8& = &-8-14-x \\\Leftrightarrow & -20x \color{red}{-8} & = &-22 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &-22 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & -20x+x& = &-22+8 \\\Leftrightarrow & -19x& = &-14 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-14}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{14}{19} & & \\ & V = \left\{ \frac{14}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (x+7)& = & 5 \color{red}{+} (-5+2x) \\\Leftrightarrow & 5x+35& = &5-5+2x \\\Leftrightarrow & 5x \color{red}{+35} & = &0 \color{red}{+2x} \\\Leftrightarrow & 5x \color{red}{+35} \color{blue}{-35} \color{blue}{-2x} & = &0 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-35} \\\Leftrightarrow & 5x-2x& = &0-35 \\\Leftrightarrow & 3x& = &-35 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-35}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-35}{3} & & \\ & V = \left\{ \frac{-35}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (4x+2)& = & -11 \color{red}{-} (1+x) \\\Leftrightarrow & 20x+10& = &-11-1-x \\\Leftrightarrow & 20x \color{red}{+10} & = &-12 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & 20x+x& = &-12-10 \\\Leftrightarrow & 21x& = &-22 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-22}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-22}{21} & & \\ & V = \left\{ \frac{-22}{21} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (2x-3)& = & 1 \color{red}{+} (15+x) \\\Leftrightarrow & 10x-15& = &1+15+x \\\Leftrightarrow & 10x \color{red}{-15} & = &16 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &16 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & 10x-x& = &16+15 \\\Leftrightarrow & 9x& = &31 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{31}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{31}{9} & & \\ & V = \left\{ \frac{31}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-2x+6)& = & -1 \color{red}{+} (-9+x) \\\Leftrightarrow & -8x+24& = &-1-9+x \\\Leftrightarrow & -8x \color{red}{+24} & = &-10 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & -8x-x& = &-10-24 \\\Leftrightarrow & -9x& = &-34 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-34}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{34}{9} & & \\ & V = \left\{ \frac{34}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (5x+7)& = & -9 \color{red}{-} (-1+4x) \\\Leftrightarrow & 15x+21& = &-9+1-4x \\\Leftrightarrow & 15x \color{red}{+21} & = &-8 \color{red}{-4x} \\\Leftrightarrow & 15x \color{red}{+21} \color{blue}{-21} \color{blue}{+4x} & = &-8 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-21} \\\Leftrightarrow & 15x+4x& = &-8-21 \\\Leftrightarrow & 19x& = &-29 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-29}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-29}{19} & & \\ & V = \left\{ \frac{-29}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-6x+7)& = & 13 \color{red}{-} (5+x) \\\Leftrightarrow & -24x+28& = &13-5-x \\\Leftrightarrow & -24x \color{red}{+28} & = &8 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+28} \color{blue}{-28} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{-28} \\\Leftrightarrow & -24x+x& = &8-28 \\\Leftrightarrow & -23x& = &-20 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-20}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{20}{23} & & \\ & V = \left\{ \frac{20}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (3x-2)& = & -11 \color{red}{-} (-7+x) \\\Leftrightarrow & 12x-8& = &-11+7-x \\\Leftrightarrow & 12x \color{red}{-8} & = &-4 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 12x+x& = &-4+8 \\\Leftrightarrow & 13x& = &4 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{4}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{4}{13} & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)