Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (3x+3)& = & -7 \color{red}{+} (6+x) \\\Leftrightarrow & 18x+18& = &-7+6+x \\\Leftrightarrow & 18x \color{red}{+18} & = &-1 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & 18x-x& = &-1-18 \\\Leftrightarrow & 17x& = &-19 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-19}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-19}{17} & & \\ & V = \left\{ \frac{-19}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (6x+3)& = & 7 \color{red}{+} (10+x) \\\Leftrightarrow & 30x+15& = &7+10+x \\\Leftrightarrow & 30x \color{red}{+15} & = &17 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &17 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & 30x-x& = &17-15 \\\Leftrightarrow & 29x& = &2 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{2}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{2}{29} & & \\ & V = \left\{ \frac{2}{29} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (5x+6)& = & -10 \color{red}{-} (-14+x) \\\Leftrightarrow & 30x+36& = &-10+14-x \\\Leftrightarrow & 30x \color{red}{+36} & = &4 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & 30x+x& = &4-36 \\\Leftrightarrow & 31x& = &-32 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-32}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-32}{31} & & \\ & V = \left\{ \frac{-32}{31} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (4x-1)& = & -9 \color{red}{-} (-12+x) \\\Leftrightarrow & 24x-6& = &-9+12-x \\\Leftrightarrow & 24x \color{red}{-6} & = &3 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 24x+x& = &3+6 \\\Leftrightarrow & 25x& = &9 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{9}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{9}{25} & & \\ & V = \left\{ \frac{9}{25} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-5x+6)& = & 8 \color{red}{+} (-14-3x) \\\Leftrightarrow & -10x+12& = &8-14-3x \\\Leftrightarrow & -10x \color{red}{+12} & = &-6 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{+12} \color{blue}{-12} \color{blue}{+3x} & = &-6 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-12} \\\Leftrightarrow & -10x+3x& = &-6-12 \\\Leftrightarrow & -7x& = &-18 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-18}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{18}{7} & & \\ & V = \left\{ \frac{18}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-5x+2)& = & 6 \color{red}{-} (-14-4x) \\\Leftrightarrow & -25x+10& = &6+14+4x \\\Leftrightarrow & -25x \color{red}{+10} & = &20 \color{red}{+4x} \\\Leftrightarrow & -25x \color{red}{+10} \color{blue}{-10} \color{blue}{-4x} & = &20 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-10} \\\Leftrightarrow & -25x-4x& = &20-10 \\\Leftrightarrow & -29x& = &10 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{10}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-10}{29} & & \\ & V = \left\{ \frac{-10}{29} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (4x+3)& = & -5 \color{red}{-} (-13+x) \\\Leftrightarrow & 12x+9& = &-5+13-x \\\Leftrightarrow & 12x \color{red}{+9} & = &8 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+9} \color{blue}{-9} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{-9} \\\Leftrightarrow & 12x+x& = &8-9 \\\Leftrightarrow & 13x& = &-1 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-1}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-1}{13} & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (6x+6)& = & -1 \color{red}{-} (14+x) \\\Leftrightarrow & 24x+24& = &-1-14-x \\\Leftrightarrow & 24x \color{red}{+24} & = &-15 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-15 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 24x+x& = &-15-24 \\\Leftrightarrow & 25x& = &-39 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-39}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-39}{25} & & \\ & V = \left\{ \frac{-39}{25} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-5x-3)& = & -5 \color{red}{-} (-14+x) \\\Leftrightarrow & -30x-18& = &-5+14-x \\\Leftrightarrow & -30x \color{red}{-18} & = &9 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & -30x+x& = &9+18 \\\Leftrightarrow & -29x& = &27 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{27}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-27}{29} & & \\ & V = \left\{ \frac{-27}{29} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (2x-4)& = & 10 \color{red}{-} (-9-3x) \\\Leftrightarrow & 10x-20& = &10+9+3x \\\Leftrightarrow & 10x \color{red}{-20} & = &19 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{-20} \color{blue}{+20} \color{blue}{-3x} & = &19 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+20} \\\Leftrightarrow & 10x-3x& = &19+20 \\\Leftrightarrow & 7x& = &39 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{39}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{39}{7} & & \\ & V = \left\{ \frac{39}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-2x+6)& = & -1 \color{red}{+} (-2+x) \\\Leftrightarrow & -8x+24& = &-1-2+x \\\Leftrightarrow & -8x \color{red}{+24} & = &-3 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & -8x-x& = &-3-24 \\\Leftrightarrow & -9x& = &-27 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-27}{ \color{red}{-9} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (4x+4)& = & 11 \color{red}{-} (-15+x) \\\Leftrightarrow & 20x+20& = &11+15-x \\\Leftrightarrow & 20x \color{red}{+20} & = &26 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &26 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & 20x+x& = &26-20 \\\Leftrightarrow & 21x& = &6 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{6}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{2}{7} & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)