Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (6x+2)& = & -10 \color{red}{+} (-15+x) \\\Leftrightarrow & 12x+4& = &-10-15+x \\\Leftrightarrow & 12x \color{red}{+4} & = &-25 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &-25 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & 12x-x& = &-25-4 \\\Leftrightarrow & 11x& = &-29 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-29}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-29}{11} & & \\ & V = \left\{ \frac{-29}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (x-1)& = & -5 \color{red}{+} (-5+4x) \\\Leftrightarrow & 3x-3& = &-5-5+4x \\\Leftrightarrow & 3x \color{red}{-3} & = &-10 \color{red}{+4x} \\\Leftrightarrow & 3x \color{red}{-3} \color{blue}{+3} \color{blue}{-4x} & = &-10 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+3} \\\Leftrightarrow & 3x-4x& = &-10+3 \\\Leftrightarrow & -x& = &-7 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-7}{ \color{red}{-1} } \\\Leftrightarrow & x = 7 & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-6x+7)& = & -1 \color{red}{+} (-2+x) \\\Leftrightarrow & -24x+28& = &-1-2+x \\\Leftrightarrow & -24x \color{red}{+28} & = &-3 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & -24x-x& = &-3-28 \\\Leftrightarrow & -25x& = &-31 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-31}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{31}{25} & & \\ & V = \left\{ \frac{31}{25} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (x+3)& = & -7 \color{red}{+} (-7+3x) \\\Leftrightarrow & 4x+12& = &-7-7+3x \\\Leftrightarrow & 4x \color{red}{+12} & = &-14 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+12} \color{blue}{-12} \color{blue}{-3x} & = &-14 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-12} \\\Leftrightarrow & 4x-3x& = &-14-12 \\\Leftrightarrow & x& = &-26 \\ & V = \left\{ -26 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (6x+5)& = & 13 \color{red}{-} (-1+x) \\\Leftrightarrow & 12x+10& = &13+1-x \\\Leftrightarrow & 12x \color{red}{+10} & = &14 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & 12x+x& = &14-10 \\\Leftrightarrow & 13x& = &4 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{4}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{4}{13} & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (5x-2)& = & 8 \color{red}{+} (-7+3x) \\\Leftrightarrow & 20x-8& = &8-7+3x \\\Leftrightarrow & 20x \color{red}{-8} & = &1 \color{red}{+3x} \\\Leftrightarrow & 20x \color{red}{-8} \color{blue}{+8} \color{blue}{-3x} & = &1 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+8} \\\Leftrightarrow & 20x-3x& = &1+8 \\\Leftrightarrow & 17x& = &9 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{9}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{9}{17} & & \\ & V = \left\{ \frac{9}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-5x-3)& = & 10 \color{red}{+} (10-3x) \\\Leftrightarrow & -10x-6& = &10+10-3x \\\Leftrightarrow & -10x \color{red}{-6} & = &20 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{-6} \color{blue}{+6} \color{blue}{+3x} & = &20 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+6} \\\Leftrightarrow & -10x+3x& = &20+6 \\\Leftrightarrow & -7x& = &26 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{26}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-26}{7} & & \\ & V = \left\{ \frac{-26}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-6x-6)& = & -10 \color{red}{+} (-5+x) \\\Leftrightarrow & -30x-30& = &-10-5+x \\\Leftrightarrow & -30x \color{red}{-30} & = &-15 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & -30x-x& = &-15+30 \\\Leftrightarrow & -31x& = &15 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{15}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-15}{31} & & \\ & V = \left\{ \frac{-15}{31} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-3x-6)& = & -9 \color{red}{-} (3+x) \\\Leftrightarrow & -9x-18& = &-9-3-x \\\Leftrightarrow & -9x \color{red}{-18} & = &-12 \color{red}{-x} \\\Leftrightarrow & -9x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & -9x+x& = &-12+18 \\\Leftrightarrow & -8x& = &6 \\\Leftrightarrow & \frac{-8x}{ \color{red}{-8} }& = &\frac{6}{ \color{red}{-8} } \\\Leftrightarrow & x = \frac{-3}{4} & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-2x-1)& = & 5 \color{red}{-} (12-3x) \\\Leftrightarrow & -4x-2& = &5-12+3x \\\Leftrightarrow & -4x \color{red}{-2} & = &-7 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-2} \color{blue}{+2} \color{blue}{-3x} & = &-7 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+2} \\\Leftrightarrow & -4x-3x& = &-7+2 \\\Leftrightarrow & -7x& = &-5 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-5}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{5}{7} & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (2x-1)& = & 7 \color{red}{+} (11+x) \\\Leftrightarrow & 8x-4& = &7+11+x \\\Leftrightarrow & 8x \color{red}{-4} & = &18 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &18 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & 8x-x& = &18+4 \\\Leftrightarrow & 7x& = &22 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{22}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{22}{7} & & \\ & V = \left\{ \frac{22}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-3x+5)& = & 10 \color{red}{+} (-8-5x) \\\Leftrightarrow & -18x+30& = &10-8-5x \\\Leftrightarrow & -18x \color{red}{+30} & = &2 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{+30} \color{blue}{-30} \color{blue}{+5x} & = &2 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-30} \\\Leftrightarrow & -18x+5x& = &2-30 \\\Leftrightarrow & -13x& = &-28 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-28}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{28}{13} & & \\ & V = \left\{ \frac{28}{13} \right\} & \\\end{align}\)