Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (5x+1)& = & 2 \color{red}{-} (13+x) \\\Leftrightarrow & 10x+2& = &2-13-x \\\Leftrightarrow & 10x \color{red}{+2} & = &-11 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{+2} \color{blue}{-2} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{-2} \\\Leftrightarrow & 10x+x& = &-11-2 \\\Leftrightarrow & 11x& = &-13 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-13}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-13}{11} & & \\ & V = \left\{ \frac{-13}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (4x+6)& = & 14 \color{red}{-} (-9+x) \\\Leftrightarrow & 24x+36& = &14+9-x \\\Leftrightarrow & 24x \color{red}{+36} & = &23 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &23 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & 24x+x& = &23-36 \\\Leftrightarrow & 25x& = &-13 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-13}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-13}{25} & & \\ & V = \left\{ \frac{-13}{25} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (6x-1)& = & 3 \color{red}{-} (-6+x) \\\Leftrightarrow & 12x-2& = &3+6-x \\\Leftrightarrow & 12x \color{red}{-2} & = &9 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-2} \color{blue}{+2} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{+2} \\\Leftrightarrow & 12x+x& = &9+2 \\\Leftrightarrow & 13x& = &11 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{11}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{11}{13} & & \\ & V = \left\{ \frac{11}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-5x-1)& = & -7 \color{red}{-} (9-2x) \\\Leftrightarrow & -25x-5& = &-7-9+2x \\\Leftrightarrow & -25x \color{red}{-5} & = &-16 \color{red}{+2x} \\\Leftrightarrow & -25x \color{red}{-5} \color{blue}{+5} \color{blue}{-2x} & = &-16 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+5} \\\Leftrightarrow & -25x-2x& = &-16+5 \\\Leftrightarrow & -27x& = &-11 \\\Leftrightarrow & \frac{-27x}{ \color{red}{-27} }& = &\frac{-11}{ \color{red}{-27} } \\\Leftrightarrow & x = \frac{11}{27} & & \\ & V = \left\{ \frac{11}{27} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (4x+5)& = & 5 \color{red}{+} (3+x) \\\Leftrightarrow & 12x+15& = &5+3+x \\\Leftrightarrow & 12x \color{red}{+15} & = &8 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & 12x-x& = &8-15 \\\Leftrightarrow & 11x& = &-7 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-7}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-7}{11} & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (2x-3)& = & -3 \color{red}{+} (2+3x) \\\Leftrightarrow & 4x-6& = &-3+2+3x \\\Leftrightarrow & 4x \color{red}{-6} & = &-1 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{-6} \color{blue}{+6} \color{blue}{-3x} & = &-1 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+6} \\\Leftrightarrow & 4x-3x& = &-1+6 \\\Leftrightarrow & x& = &5 \\ & V = \left\{ 5 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-6x+5)& = & 2 \color{red}{+} (10-5x) \\\Leftrightarrow & -36x+30& = &2+10-5x \\\Leftrightarrow & -36x \color{red}{+30} & = &12 \color{red}{-5x} \\\Leftrightarrow & -36x \color{red}{+30} \color{blue}{-30} \color{blue}{+5x} & = &12 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-30} \\\Leftrightarrow & -36x+5x& = &12-30 \\\Leftrightarrow & -31x& = &-18 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-18}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{18}{31} & & \\ & V = \left\{ \frac{18}{31} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-4x+2)& = & -12 \color{red}{-} (8+x) \\\Leftrightarrow & -8x+4& = &-12-8-x \\\Leftrightarrow & -8x \color{red}{+4} & = &-20 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-20 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & -8x+x& = &-20-4 \\\Leftrightarrow & -7x& = &-24 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-24}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{24}{7} & & \\ & V = \left\{ \frac{24}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-5x-2)& = & -13 \color{red}{-} (1+2x) \\\Leftrightarrow & -25x-10& = &-13-1-2x \\\Leftrightarrow & -25x \color{red}{-10} & = &-14 \color{red}{-2x} \\\Leftrightarrow & -25x \color{red}{-10} \color{blue}{+10} \color{blue}{+2x} & = &-14 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+10} \\\Leftrightarrow & -25x+2x& = &-14+10 \\\Leftrightarrow & -23x& = &-4 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-4}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{4}{23} & & \\ & V = \left\{ \frac{4}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (3x+1)& = & 8 \color{red}{+} (-14+x) \\\Leftrightarrow & 12x+4& = &8-14+x \\\Leftrightarrow & 12x \color{red}{+4} & = &-6 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & 12x-x& = &-6-4 \\\Leftrightarrow & 11x& = &-10 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-10}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-10}{11} & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-4x-1)& = & 15 \color{red}{-} (-15+x) \\\Leftrightarrow & -24x-6& = &15+15-x \\\Leftrightarrow & -24x \color{red}{-6} & = &30 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &30 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -24x+x& = &30+6 \\\Leftrightarrow & -23x& = &36 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{36}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-36}{23} & & \\ & V = \left\{ \frac{-36}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-4x-7)& = & -14 \color{red}{-} (4+x) \\\Leftrightarrow & -24x-42& = &-14-4-x \\\Leftrightarrow & -24x \color{red}{-42} & = &-18 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &-18 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & -24x+x& = &-18+42 \\\Leftrightarrow & -23x& = &24 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{24}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-24}{23} & & \\ & V = \left\{ \frac{-24}{23} \right\} & \\\end{align}\)