Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-2x-1)& = & 3 \color{red}{-} (-5-5x) \\\Leftrightarrow & -6x-3& = &3+5+5x \\\Leftrightarrow & -6x \color{red}{-3} & = &8 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-3} \color{blue}{+3} \color{blue}{-5x} & = &8 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+3} \\\Leftrightarrow & -6x-5x& = &8+3 \\\Leftrightarrow & -11x& = &11 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{11}{ \color{red}{-11} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-4x-1)& = & -13 \color{red}{+} (-8-5x) \\\Leftrightarrow & -16x-4& = &-13-8-5x \\\Leftrightarrow & -16x \color{red}{-4} & = &-21 \color{red}{-5x} \\\Leftrightarrow & -16x \color{red}{-4} \color{blue}{+4} \color{blue}{+5x} & = &-21 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+4} \\\Leftrightarrow & -16x+5x& = &-21+4 \\\Leftrightarrow & -11x& = &-17 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-17}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{17}{11} & & \\ & V = \left\{ \frac{17}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (4x-2)& = & 6 \color{red}{+} (-1+x) \\\Leftrightarrow & 12x-6& = &6-1+x \\\Leftrightarrow & 12x \color{red}{-6} & = &5 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 12x-x& = &5+6 \\\Leftrightarrow & 11x& = &11 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{11}{ \color{red}{11} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (4x-3)& = & 12 \color{red}{-} (-2+x) \\\Leftrightarrow & 20x-15& = &12+2-x \\\Leftrightarrow & 20x \color{red}{-15} & = &14 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & 20x+x& = &14+15 \\\Leftrightarrow & 21x& = &29 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{29}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{29}{21} & & \\ & V = \left\{ \frac{29}{21} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-3x+4)& = & -2 \color{red}{+} (9-5x) \\\Leftrightarrow & -6x+8& = &-2+9-5x \\\Leftrightarrow & -6x \color{red}{+8} & = &7 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{+8} \color{blue}{-8} \color{blue}{+5x} & = &7 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-8} \\\Leftrightarrow & -6x+5x& = &7-8 \\\Leftrightarrow & -x& = &-1 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-1}{ \color{red}{-1} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (4x-2)& = & 12 \color{red}{+} (1+x) \\\Leftrightarrow & 24x-12& = &12+1+x \\\Leftrightarrow & 24x \color{red}{-12} & = &13 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 24x-x& = &13+12 \\\Leftrightarrow & 23x& = &25 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{25}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{25}{23} & & \\ & V = \left\{ \frac{25}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-x-6)& = & 14 \color{red}{-} (-13-4x) \\\Leftrightarrow & -5x-30& = &14+13+4x \\\Leftrightarrow & -5x \color{red}{-30} & = &27 \color{red}{+4x} \\\Leftrightarrow & -5x \color{red}{-30} \color{blue}{+30} \color{blue}{-4x} & = &27 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+30} \\\Leftrightarrow & -5x-4x& = &27+30 \\\Leftrightarrow & -9x& = &57 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{57}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-19}{3} & & \\ & V = \left\{ \frac{-19}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-6x-1)& = & -2 \color{red}{+} (-11+x) \\\Leftrightarrow & -36x-6& = &-2-11+x \\\Leftrightarrow & -36x \color{red}{-6} & = &-13 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-13 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -36x-x& = &-13+6 \\\Leftrightarrow & -37x& = &-7 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{-7}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{7}{37} & & \\ & V = \left\{ \frac{7}{37} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (5x-7)& = & -2 \color{red}{-} (14+x) \\\Leftrightarrow & 25x-35& = &-2-14-x \\\Leftrightarrow & 25x \color{red}{-35} & = &-16 \color{red}{-x} \\\Leftrightarrow & 25x \color{red}{-35} \color{blue}{+35} \color{blue}{+x} & = &-16 \color{red}{-x} \color{blue}{+x} \color{blue}{+35} \\\Leftrightarrow & 25x+x& = &-16+35 \\\Leftrightarrow & 26x& = &19 \\\Leftrightarrow & \frac{26x}{ \color{red}{26} }& = &\frac{19}{ \color{red}{26} } \\\Leftrightarrow & x = \frac{19}{26} & & \\ & V = \left\{ \frac{19}{26} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-2x+4)& = & -4 \color{red}{-} (-7+x) \\\Leftrightarrow & -10x+20& = &-4+7-x \\\Leftrightarrow & -10x \color{red}{+20} & = &3 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & -10x+x& = &3-20 \\\Leftrightarrow & -9x& = &-17 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-17}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{17}{9} & & \\ & V = \left\{ \frac{17}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (4x-1)& = & -12 \color{red}{-} (-11-3x) \\\Leftrightarrow & 16x-4& = &-12+11+3x \\\Leftrightarrow & 16x \color{red}{-4} & = &-1 \color{red}{+3x} \\\Leftrightarrow & 16x \color{red}{-4} \color{blue}{+4} \color{blue}{-3x} & = &-1 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+4} \\\Leftrightarrow & 16x-3x& = &-1+4 \\\Leftrightarrow & 13x& = &3 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{3}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{3}{13} & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (5x-4)& = & -9 \color{red}{-} (10+x) \\\Leftrightarrow & 30x-24& = &-9-10-x \\\Leftrightarrow & 30x \color{red}{-24} & = &-19 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 30x+x& = &-19+24 \\\Leftrightarrow & 31x& = &5 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{5}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{5}{31} & & \\ & V = \left\{ \frac{5}{31} \right\} & \\\end{align}\)