Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (6x+4)& = & 3 \color{red}{-} (1+x) \\\Leftrightarrow & 18x+12& = &3-1-x \\\Leftrightarrow & 18x \color{red}{+12} & = &2 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 18x+x& = &2-12 \\\Leftrightarrow & 19x& = &-10 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-10}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-10}{19} & & \\ & V = \left\{ \frac{-10}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (4x+4)& = & 5 \color{red}{-} (-4+3x) \\\Leftrightarrow & 20x+20& = &5+4-3x \\\Leftrightarrow & 20x \color{red}{+20} & = &9 \color{red}{-3x} \\\Leftrightarrow & 20x \color{red}{+20} \color{blue}{-20} \color{blue}{+3x} & = &9 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-20} \\\Leftrightarrow & 20x+3x& = &9-20 \\\Leftrightarrow & 23x& = &-11 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-11}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-11}{23} & & \\ & V = \left\{ \frac{-11}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-3x+3)& = & 12 \color{red}{+} (-3+x) \\\Leftrightarrow & -12x+12& = &12-3+x \\\Leftrightarrow & -12x \color{red}{+12} & = &9 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -12x-x& = &9-12 \\\Leftrightarrow & -13x& = &-3 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-3}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{3}{13} & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (5x-2)& = & 9 \color{red}{+} (10+x) \\\Leftrightarrow & 30x-12& = &9+10+x \\\Leftrightarrow & 30x \color{red}{-12} & = &19 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &19 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 30x-x& = &19+12 \\\Leftrightarrow & 29x& = &31 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{31}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{31}{29} & & \\ & V = \left\{ \frac{31}{29} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-5x-3)& = & -13 \color{red}{-} (-9-4x) \\\Leftrightarrow & -25x-15& = &-13+9+4x \\\Leftrightarrow & -25x \color{red}{-15} & = &-4 \color{red}{+4x} \\\Leftrightarrow & -25x \color{red}{-15} \color{blue}{+15} \color{blue}{-4x} & = &-4 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+15} \\\Leftrightarrow & -25x-4x& = &-4+15 \\\Leftrightarrow & -29x& = &11 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{11}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-11}{29} & & \\ & V = \left\{ \frac{-11}{29} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (x+2)& = & -13 \color{red}{+} (12+x) \\\Leftrightarrow & 6x+12& = &-13+12+x \\\Leftrightarrow & 6x \color{red}{+12} & = &-1 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 6x-x& = &-1-12 \\\Leftrightarrow & 5x& = &-13 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-13}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-13}{5} & & \\ & V = \left\{ \frac{-13}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (3x+7)& = & 10 \color{red}{-} (-13-4x) \\\Leftrightarrow & 9x+21& = &10+13+4x \\\Leftrightarrow & 9x \color{red}{+21} & = &23 \color{red}{+4x} \\\Leftrightarrow & 9x \color{red}{+21} \color{blue}{-21} \color{blue}{-4x} & = &23 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-21} \\\Leftrightarrow & 9x-4x& = &23-21 \\\Leftrightarrow & 5x& = &2 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{2}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{2}{5} & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (2x+3)& = & 9 \color{red}{-} (-15-3x) \\\Leftrightarrow & 4x+6& = &9+15+3x \\\Leftrightarrow & 4x \color{red}{+6} & = &24 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+6} \color{blue}{-6} \color{blue}{-3x} & = &24 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-6} \\\Leftrightarrow & 4x-3x& = &24-6 \\\Leftrightarrow & x& = &18 \\ & V = \left\{ 18 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (4x-6)& = & 3 \color{red}{+} (8-3x) \\\Leftrightarrow & 16x-24& = &3+8-3x \\\Leftrightarrow & 16x \color{red}{-24} & = &11 \color{red}{-3x} \\\Leftrightarrow & 16x \color{red}{-24} \color{blue}{+24} \color{blue}{+3x} & = &11 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+24} \\\Leftrightarrow & 16x+3x& = &11+24 \\\Leftrightarrow & 19x& = &35 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{35}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{35}{19} & & \\ & V = \left\{ \frac{35}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (3x+5)& = & 15 \color{red}{-} (-6+x) \\\Leftrightarrow & 12x+20& = &15+6-x \\\Leftrightarrow & 12x \color{red}{+20} & = &21 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &21 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & 12x+x& = &21-20 \\\Leftrightarrow & 13x& = &1 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{1}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{1}{13} & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-6x+7)& = & 7 \color{red}{-} (7-5x) \\\Leftrightarrow & -36x+42& = &7-7+5x \\\Leftrightarrow & -36x \color{red}{+42} & = &0 \color{red}{+5x} \\\Leftrightarrow & -36x \color{red}{+42} \color{blue}{-42} \color{blue}{-5x} & = &0 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-42} \\\Leftrightarrow & -36x-5x& = &0-42 \\\Leftrightarrow & -41x& = &-42 \\\Leftrightarrow & \frac{-41x}{ \color{red}{-41} }& = &\frac{-42}{ \color{red}{-41} } \\\Leftrightarrow & x = \frac{42}{41} & & \\ & V = \left\{ \frac{42}{41} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-4x-2)& = & 4 \color{red}{+} (-2+x) \\\Leftrightarrow & -24x-12& = &4-2+x \\\Leftrightarrow & -24x \color{red}{-12} & = &2 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -24x-x& = &2+12 \\\Leftrightarrow & -25x& = &14 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{14}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-14}{25} & & \\ & V = \left\{ \frac{-14}{25} \right\} & \\\end{align}\)