Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-4x+1)& = & 11 \color{red}{-} (13+x) \\\Leftrightarrow & -24x+6& = &11-13-x \\\Leftrightarrow & -24x \color{red}{+6} & = &-2 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -24x+x& = &-2-6 \\\Leftrightarrow & -23x& = &-8 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-8}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{8}{23} & & \\ & V = \left\{ \frac{8}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (4x+2)& = & 14 \color{red}{+} (-13+x) \\\Leftrightarrow & 20x+10& = &14-13+x \\\Leftrightarrow & 20x \color{red}{+10} & = &1 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & 20x-x& = &1-10 \\\Leftrightarrow & 19x& = &-9 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-9}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-9}{19} & & \\ & V = \left\{ \frac{-9}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-6x-3)& = & 3 \color{red}{+} (-13+x) \\\Leftrightarrow & -12x-6& = &3-13+x \\\Leftrightarrow & -12x \color{red}{-6} & = &-10 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -12x-x& = &-10+6 \\\Leftrightarrow & -13x& = &-4 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-4}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{4}{13} & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (x-4)& = & 8 \color{red}{+} (3+x) \\\Leftrightarrow & 4x-16& = &8+3+x \\\Leftrightarrow & 4x \color{red}{-16} & = &11 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{-16} \color{blue}{+16} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{+16} \\\Leftrightarrow & 4x-x& = &11+16 \\\Leftrightarrow & 3x& = &27 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{27}{ \color{red}{3} } \\\Leftrightarrow & x = 9 & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-x+7)& = & 2 \color{red}{+} (-11-4x) \\\Leftrightarrow & -5x+35& = &2-11-4x \\\Leftrightarrow & -5x \color{red}{+35} & = &-9 \color{red}{-4x} \\\Leftrightarrow & -5x \color{red}{+35} \color{blue}{-35} \color{blue}{+4x} & = &-9 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-35} \\\Leftrightarrow & -5x+4x& = &-9-35 \\\Leftrightarrow & -x& = &-44 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-44}{ \color{red}{-1} } \\\Leftrightarrow & x = 44 & & \\ & V = \left\{ 44 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (3x+1)& = & -10 \color{red}{+} (11+2x) \\\Leftrightarrow & 9x+3& = &-10+11+2x \\\Leftrightarrow & 9x \color{red}{+3} & = &1 \color{red}{+2x} \\\Leftrightarrow & 9x \color{red}{+3} \color{blue}{-3} \color{blue}{-2x} & = &1 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-3} \\\Leftrightarrow & 9x-2x& = &1-3 \\\Leftrightarrow & 7x& = &-2 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-2}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-2}{7} & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-6x-4)& = & -9 \color{red}{+} (6+x) \\\Leftrightarrow & -36x-24& = &-9+6+x \\\Leftrightarrow & -36x \color{red}{-24} & = &-3 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -36x-x& = &-3+24 \\\Leftrightarrow & -37x& = &21 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{21}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{-21}{37} & & \\ & V = \left\{ \frac{-21}{37} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-x+2)& = & -8 \color{red}{+} (-1-5x) \\\Leftrightarrow & -6x+12& = &-8-1-5x \\\Leftrightarrow & -6x \color{red}{+12} & = &-9 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{+12} \color{blue}{-12} \color{blue}{+5x} & = &-9 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-12} \\\Leftrightarrow & -6x+5x& = &-9-12 \\\Leftrightarrow & -x& = &-21 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-21}{ \color{red}{-1} } \\\Leftrightarrow & x = 21 & & \\ & V = \left\{ 21 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (6x-4)& = & -7 \color{red}{-} (-7-5x) \\\Leftrightarrow & 36x-24& = &-7+7+5x \\\Leftrightarrow & 36x \color{red}{-24} & = &0 \color{red}{+5x} \\\Leftrightarrow & 36x \color{red}{-24} \color{blue}{+24} \color{blue}{-5x} & = &0 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+24} \\\Leftrightarrow & 36x-5x& = &0+24 \\\Leftrightarrow & 31x& = &24 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{24}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{24}{31} & & \\ & V = \left\{ \frac{24}{31} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (x-1)& = & 15 \color{red}{+} (2+x) \\\Leftrightarrow & 4x-4& = &15+2+x \\\Leftrightarrow & 4x \color{red}{-4} & = &17 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &17 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & 4x-x& = &17+4 \\\Leftrightarrow & 3x& = &21 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{21}{ \color{red}{3} } \\\Leftrightarrow & x = 7 & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (2x-3)& = & 13 \color{red}{+} (6-5x) \\\Leftrightarrow & 8x-12& = &13+6-5x \\\Leftrightarrow & 8x \color{red}{-12} & = &19 \color{red}{-5x} \\\Leftrightarrow & 8x \color{red}{-12} \color{blue}{+12} \color{blue}{+5x} & = &19 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+12} \\\Leftrightarrow & 8x+5x& = &19+12 \\\Leftrightarrow & 13x& = &31 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{31}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{31}{13} & & \\ & V = \left\{ \frac{31}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-3x+6)& = & 6 \color{red}{+} (-6+4x) \\\Leftrightarrow & -9x+18& = &6-6+4x \\\Leftrightarrow & -9x \color{red}{+18} & = &0 \color{red}{+4x} \\\Leftrightarrow & -9x \color{red}{+18} \color{blue}{-18} \color{blue}{-4x} & = &0 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-18} \\\Leftrightarrow & -9x-4x& = &0-18 \\\Leftrightarrow & -13x& = &-18 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-18}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{18}{13} & & \\ & V = \left\{ \frac{18}{13} \right\} & \\\end{align}\)