Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-4x+3)& = & 10 \color{red}{-} (-3+x) \\\Leftrightarrow & -12x+9& = &10+3-x \\\Leftrightarrow & -12x \color{red}{+9} & = &13 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+9} \color{blue}{-9} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{-9} \\\Leftrightarrow & -12x+x& = &13-9 \\\Leftrightarrow & -11x& = &4 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{4}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-4}{11} & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (x+3)& = & -13 \color{red}{-} (-10+4x) \\\Leftrightarrow & 3x+9& = &-13+10-4x \\\Leftrightarrow & 3x \color{red}{+9} & = &-3 \color{red}{-4x} \\\Leftrightarrow & 3x \color{red}{+9} \color{blue}{-9} \color{blue}{+4x} & = &-3 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-9} \\\Leftrightarrow & 3x+4x& = &-3-9 \\\Leftrightarrow & 7x& = &-12 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-12}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-12}{7} & & \\ & V = \left\{ \frac{-12}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-5x-2)& = & -4 \color{red}{+} (-4+x) \\\Leftrightarrow & -30x-12& = &-4-4+x \\\Leftrightarrow & -30x \color{red}{-12} & = &-8 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -30x-x& = &-8+12 \\\Leftrightarrow & -31x& = &4 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{4}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-4}{31} & & \\ & V = \left\{ \frac{-4}{31} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (4x+2)& = & -13 \color{red}{-} (15+3x) \\\Leftrightarrow & 20x+10& = &-13-15-3x \\\Leftrightarrow & 20x \color{red}{+10} & = &-28 \color{red}{-3x} \\\Leftrightarrow & 20x \color{red}{+10} \color{blue}{-10} \color{blue}{+3x} & = &-28 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-10} \\\Leftrightarrow & 20x+3x& = &-28-10 \\\Leftrightarrow & 23x& = &-38 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-38}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-38}{23} & & \\ & V = \left\{ \frac{-38}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-x-6)& = & 12 \color{red}{+} (15+x) \\\Leftrightarrow & -5x-30& = &12+15+x \\\Leftrightarrow & -5x \color{red}{-30} & = &27 \color{red}{+x} \\\Leftrightarrow & -5x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &27 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & -5x-x& = &27+30 \\\Leftrightarrow & -6x& = &57 \\\Leftrightarrow & \frac{-6x}{ \color{red}{-6} }& = &\frac{57}{ \color{red}{-6} } \\\Leftrightarrow & x = \frac{-19}{2} & & \\ & V = \left\{ \frac{-19}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-6x-3)& = & -8 \color{red}{-} (1+x) \\\Leftrightarrow & -30x-15& = &-8-1-x \\\Leftrightarrow & -30x \color{red}{-15} & = &-9 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & -30x+x& = &-9+15 \\\Leftrightarrow & -29x& = &6 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{6}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-6}{29} & & \\ & V = \left\{ \frac{-6}{29} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-4x+1)& = & -13 \color{red}{-} (-7+x) \\\Leftrightarrow & -24x+6& = &-13+7-x \\\Leftrightarrow & -24x \color{red}{+6} & = &-6 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -24x+x& = &-6-6 \\\Leftrightarrow & -23x& = &-12 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-12}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{12}{23} & & \\ & V = \left\{ \frac{12}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (5x-6)& = & -3 \color{red}{-} (3+x) \\\Leftrightarrow & 25x-30& = &-3-3-x \\\Leftrightarrow & 25x \color{red}{-30} & = &-6 \color{red}{-x} \\\Leftrightarrow & 25x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 25x+x& = &-6+30 \\\Leftrightarrow & 26x& = &24 \\\Leftrightarrow & \frac{26x}{ \color{red}{26} }& = &\frac{24}{ \color{red}{26} } \\\Leftrightarrow & x = \frac{12}{13} & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (4x-1)& = & 5 \color{red}{+} (-10-5x) \\\Leftrightarrow & 8x-2& = &5-10-5x \\\Leftrightarrow & 8x \color{red}{-2} & = &-5 \color{red}{-5x} \\\Leftrightarrow & 8x \color{red}{-2} \color{blue}{+2} \color{blue}{+5x} & = &-5 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+2} \\\Leftrightarrow & 8x+5x& = &-5+2 \\\Leftrightarrow & 13x& = &-3 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-3}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-3}{13} & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-5x+7)& = & 14 \color{red}{-} (2+x) \\\Leftrightarrow & -30x+42& = &14-2-x \\\Leftrightarrow & -30x \color{red}{+42} & = &12 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & -30x+x& = &12-42 \\\Leftrightarrow & -29x& = &-30 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-30}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{30}{29} & & \\ & V = \left\{ \frac{30}{29} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (5x+6)& = & -10 \color{red}{+} (-6+x) \\\Leftrightarrow & 20x+24& = &-10-6+x \\\Leftrightarrow & 20x \color{red}{+24} & = &-16 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-16 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 20x-x& = &-16-24 \\\Leftrightarrow & 19x& = &-40 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-40}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-40}{19} & & \\ & V = \left\{ \frac{-40}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-6x-4)& = & -4 \color{red}{+} (4+x) \\\Leftrightarrow & -36x-24& = &-4+4+x \\\Leftrightarrow & -36x \color{red}{-24} & = &0 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -36x-x& = &0+24 \\\Leftrightarrow & -37x& = &24 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{24}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{-24}{37} & & \\ & V = \left\{ \frac{-24}{37} \right\} & \\\end{align}\)