Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(4(-3x-3)=-11+(10+5x)\)
2. \(2(3x-6)=-13+(-5+5x)\)
3. \(6(-3x+3)=2+(-6-5x)\)
4. \(5(x+4)=9-(10+x)\)
5. \(5(-5x+3)=1-(1-4x)\)
6. \(6(6x-5)=-9+(-9+35x)\)
7. \(6(x-4)=-6-(-6+x)\)
8. \(4(5x+6)=-6-(-10+3x)\)
9. \(5(-4x-4)=14+(15+x)\)
10. \(5(-2x+2)=-12+(15-3x)\)
11. \(2(-5x-5)=2+(-7+3x)\)
12. \(5(2x-6)=-11-(-12+3x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-3x-3)& = & -11 \color{red}{+} (10+5x) \\\Leftrightarrow & -12x-12& = &-11+10+5x \\\Leftrightarrow & -12x \color{red}{-12} & = &-1 \color{red}{+5x} \\\Leftrightarrow & -12x \color{red}{-12} \color{blue}{+12} \color{blue}{-5x} & = &-1 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+12} \\\Leftrightarrow & -12x-5x& = &-1+12 \\\Leftrightarrow & -17x& = &11 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{11}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-11}{17} & & \\ & V = \left\{ \frac{-11}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (3x-6)& = & -13 \color{red}{+} (-5+5x) \\\Leftrightarrow & 6x-12& = &-13-5+5x \\\Leftrightarrow & 6x \color{red}{-12} & = &-18 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{-12} \color{blue}{+12} \color{blue}{-5x} & = &-18 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+12} \\\Leftrightarrow & 6x-5x& = &-18+12 \\\Leftrightarrow & x& = &-6 \\ & V = \left\{ -6 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-3x+3)& = & 2 \color{red}{+} (-6-5x) \\\Leftrightarrow & -18x+18& = &2-6-5x \\\Leftrightarrow & -18x \color{red}{+18} & = &-4 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{+18} \color{blue}{-18} \color{blue}{+5x} & = &-4 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-18} \\\Leftrightarrow & -18x+5x& = &-4-18 \\\Leftrightarrow & -13x& = &-22 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-22}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{22}{13} & & \\ & V = \left\{ \frac{22}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (x+4)& = & 9 \color{red}{-} (10+x) \\\Leftrightarrow & 5x+20& = &9-10-x \\\Leftrightarrow & 5x \color{red}{+20} & = &-1 \color{red}{-x} \\\Leftrightarrow & 5x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & 5x+x& = &-1-20 \\\Leftrightarrow & 6x& = &-21 \\\Leftrightarrow & \frac{6x}{ \color{red}{6} }& = &\frac{-21}{ \color{red}{6} } \\\Leftrightarrow & x = \frac{-7}{2} & & \\ & V = \left\{ \frac{-7}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-5x+3)& = & 1 \color{red}{-} (1-4x) \\\Leftrightarrow & -25x+15& = &1-1+4x \\\Leftrightarrow & -25x \color{red}{+15} & = &0 \color{red}{+4x} \\\Leftrightarrow & -25x \color{red}{+15} \color{blue}{-15} \color{blue}{-4x} & = &0 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-15} \\\Leftrightarrow & -25x-4x& = &0-15 \\\Leftrightarrow & -29x& = &-15 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-15}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{15}{29} & & \\ & V = \left\{ \frac{15}{29} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (6x-5)& = & -9 \color{red}{+} (-9+35x) \\\Leftrightarrow & 36x-30& = &-9-9+35x \\\Leftrightarrow & 36x \color{red}{-30} & = &-18 \color{red}{+35x} \\\Leftrightarrow & 36x \color{red}{-30} \color{blue}{+30} \color{blue}{-35x} & = &-18 \color{red}{+35x} \color{blue}{-35x} \color{blue}{+30} \\\Leftrightarrow & 36x-35x& = &-18+30 \\\Leftrightarrow & x& = &12 \\ & V = \left\{ 12 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (x-4)& = & -6 \color{red}{-} (-6+x) \\\Leftrightarrow & 6x-24& = &-6+6-x \\\Leftrightarrow & 6x \color{red}{-24} & = &0 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 6x+x& = &0+24 \\\Leftrightarrow & 7x& = &24 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{24}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{24}{7} & & \\ & V = \left\{ \frac{24}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (5x+6)& = & -6 \color{red}{-} (-10+3x) \\\Leftrightarrow & 20x+24& = &-6+10-3x \\\Leftrightarrow & 20x \color{red}{+24} & = &4 \color{red}{-3x} \\\Leftrightarrow & 20x \color{red}{+24} \color{blue}{-24} \color{blue}{+3x} & = &4 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-24} \\\Leftrightarrow & 20x+3x& = &4-24 \\\Leftrightarrow & 23x& = &-20 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-20}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-20}{23} & & \\ & V = \left\{ \frac{-20}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-4x-4)& = & 14 \color{red}{+} (15+x) \\\Leftrightarrow & -20x-20& = &14+15+x \\\Leftrightarrow & -20x \color{red}{-20} & = &29 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &29 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & -20x-x& = &29+20 \\\Leftrightarrow & -21x& = &49 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{49}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-7}{3} & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-2x+2)& = & -12 \color{red}{+} (15-3x) \\\Leftrightarrow & -10x+10& = &-12+15-3x \\\Leftrightarrow & -10x \color{red}{+10} & = &3 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{+10} \color{blue}{-10} \color{blue}{+3x} & = &3 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-10} \\\Leftrightarrow & -10x+3x& = &3-10 \\\Leftrightarrow & -7x& = &-7 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-7}{ \color{red}{-7} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-5x-5)& = & 2 \color{red}{+} (-7+3x) \\\Leftrightarrow & -10x-10& = &2-7+3x \\\Leftrightarrow & -10x \color{red}{-10} & = &-5 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{-10} \color{blue}{+10} \color{blue}{-3x} & = &-5 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+10} \\\Leftrightarrow & -10x-3x& = &-5+10 \\\Leftrightarrow & -13x& = &5 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{5}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-5}{13} & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (2x-6)& = & -11 \color{red}{-} (-12+3x) \\\Leftrightarrow & 10x-30& = &-11+12-3x \\\Leftrightarrow & 10x \color{red}{-30} & = &1 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{-30} \color{blue}{+30} \color{blue}{+3x} & = &1 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+30} \\\Leftrightarrow & 10x+3x& = &1+30 \\\Leftrightarrow & 13x& = &31 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{31}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{31}{13} & & \\ & V = \left\{ \frac{31}{13} \right\} & \\\end{align}\)