Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (2x+5)& = & 13 \color{red}{-} (2+x) \\\Leftrightarrow & 6x+15& = &13-2-x \\\Leftrightarrow & 6x \color{red}{+15} & = &11 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & 6x+x& = &11-15 \\\Leftrightarrow & 7x& = &-4 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-4}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-4}{7} & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (3x-1)& = & -11 \color{red}{-} (11+x) \\\Leftrightarrow & 18x-6& = &-11-11-x \\\Leftrightarrow & 18x \color{red}{-6} & = &-22 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-22 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 18x+x& = &-22+6 \\\Leftrightarrow & 19x& = &-16 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-16}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-16}{19} & & \\ & V = \left\{ \frac{-16}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-4x-6)& = & 8 \color{red}{+} (-2+x) \\\Leftrightarrow & -8x-12& = &8-2+x \\\Leftrightarrow & -8x \color{red}{-12} & = &6 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -8x-x& = &6+12 \\\Leftrightarrow & -9x& = &18 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{18}{ \color{red}{-9} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-x-2)& = & 2 \color{red}{+} (10-5x) \\\Leftrightarrow & -6x-12& = &2+10-5x \\\Leftrightarrow & -6x \color{red}{-12} & = &12 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-12} \color{blue}{+12} \color{blue}{+5x} & = &12 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+12} \\\Leftrightarrow & -6x+5x& = &12+12 \\\Leftrightarrow & -x& = &24 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{24}{ \color{red}{-1} } \\\Leftrightarrow & x = -24 & & \\ & V = \left\{ -24 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-6x+4)& = & -3 \color{red}{-} (3+x) \\\Leftrightarrow & -30x+20& = &-3-3-x \\\Leftrightarrow & -30x \color{red}{+20} & = &-6 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & -30x+x& = &-6-20 \\\Leftrightarrow & -29x& = &-26 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-26}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{26}{29} & & \\ & V = \left\{ \frac{26}{29} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (3x-6)& = & -10 \color{red}{-} (-6+x) \\\Leftrightarrow & 18x-36& = &-10+6-x \\\Leftrightarrow & 18x \color{red}{-36} & = &-4 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & 18x+x& = &-4+36 \\\Leftrightarrow & 19x& = &32 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{32}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{32}{19} & & \\ & V = \left\{ \frac{32}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (5x+6)& = & -9 \color{red}{+} (15-4x) \\\Leftrightarrow & 25x+30& = &-9+15-4x \\\Leftrightarrow & 25x \color{red}{+30} & = &6 \color{red}{-4x} \\\Leftrightarrow & 25x \color{red}{+30} \color{blue}{-30} \color{blue}{+4x} & = &6 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-30} \\\Leftrightarrow & 25x+4x& = &6-30 \\\Leftrightarrow & 29x& = &-24 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-24}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-24}{29} & & \\ & V = \left\{ \frac{-24}{29} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (x-6)& = & -10 \color{red}{-} (-7+3x) \\\Leftrightarrow & 4x-24& = &-10+7-3x \\\Leftrightarrow & 4x \color{red}{-24} & = &-3 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-24} \color{blue}{+24} \color{blue}{+3x} & = &-3 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+24} \\\Leftrightarrow & 4x+3x& = &-3+24 \\\Leftrightarrow & 7x& = &21 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{21}{ \color{red}{7} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-6x+2)& = & -3 \color{red}{+} (7+x) \\\Leftrightarrow & -30x+10& = &-3+7+x \\\Leftrightarrow & -30x \color{red}{+10} & = &4 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & -30x-x& = &4-10 \\\Leftrightarrow & -31x& = &-6 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-6}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{6}{31} & & \\ & V = \left\{ \frac{6}{31} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-5x-1)& = & 11 \color{red}{+} (3+x) \\\Leftrightarrow & -10x-2& = &11+3+x \\\Leftrightarrow & -10x \color{red}{-2} & = &14 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{-2} \color{blue}{+2} \color{blue}{-x} & = &14 \color{red}{+x} \color{blue}{-x} \color{blue}{+2} \\\Leftrightarrow & -10x-x& = &14+2 \\\Leftrightarrow & -11x& = &16 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{16}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-16}{11} & & \\ & V = \left\{ \frac{-16}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (6x+6)& = & -5 \color{red}{+} (-15+x) \\\Leftrightarrow & 30x+30& = &-5-15+x \\\Leftrightarrow & 30x \color{red}{+30} & = &-20 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &-20 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & 30x-x& = &-20-30 \\\Leftrightarrow & 29x& = &-50 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-50}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-50}{29} & & \\ & V = \left\{ \frac{-50}{29} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-5x-4)& = & -9 \color{red}{+} (-7+3x) \\\Leftrightarrow & -10x-8& = &-9-7+3x \\\Leftrightarrow & -10x \color{red}{-8} & = &-16 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{-8} \color{blue}{+8} \color{blue}{-3x} & = &-16 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+8} \\\Leftrightarrow & -10x-3x& = &-16+8 \\\Leftrightarrow & -13x& = &-8 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-8}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{8}{13} & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)