Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-6x-3)& = & 3 \color{red}{+} (-7+x) \\\Leftrightarrow & -24x-12& = &3-7+x \\\Leftrightarrow & -24x \color{red}{-12} & = &-4 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -24x-x& = &-4+12 \\\Leftrightarrow & -25x& = &8 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{8}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-8}{25} & & \\ & V = \left\{ \frac{-8}{25} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (2x-7)& = & -3 \color{red}{+} (2+x) \\\Leftrightarrow & 12x-42& = &-3+2+x \\\Leftrightarrow & 12x \color{red}{-42} & = &-1 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & 12x-x& = &-1+42 \\\Leftrightarrow & 11x& = &41 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{41}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{41}{11} & & \\ & V = \left\{ \frac{41}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-6x-5)& = & 11 \color{red}{-} (-9+x) \\\Leftrightarrow & -12x-10& = &11+9-x \\\Leftrightarrow & -12x \color{red}{-10} & = &20 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &20 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & -12x+x& = &20+10 \\\Leftrightarrow & -11x& = &30 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{30}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-30}{11} & & \\ & V = \left\{ \frac{-30}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-2x+6)& = & 1 \color{red}{-} (4-5x) \\\Leftrightarrow & -6x+18& = &1-4+5x \\\Leftrightarrow & -6x \color{red}{+18} & = &-3 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{+18} \color{blue}{-18} \color{blue}{-5x} & = &-3 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-18} \\\Leftrightarrow & -6x-5x& = &-3-18 \\\Leftrightarrow & -11x& = &-21 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-21}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{21}{11} & & \\ & V = \left\{ \frac{21}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-2x+5)& = & -7 \color{red}{-} (11+x) \\\Leftrightarrow & -12x+30& = &-7-11-x \\\Leftrightarrow & -12x \color{red}{+30} & = &-18 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &-18 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & -12x+x& = &-18-30 \\\Leftrightarrow & -11x& = &-48 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-48}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{48}{11} & & \\ & V = \left\{ \frac{48}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-5x-6)& = & -3 \color{red}{+} (-6+x) \\\Leftrightarrow & -30x-36& = &-3-6+x \\\Leftrightarrow & -30x \color{red}{-36} & = &-9 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-36} \color{blue}{+36} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{+36} \\\Leftrightarrow & -30x-x& = &-9+36 \\\Leftrightarrow & -31x& = &27 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{27}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-27}{31} & & \\ & V = \left\{ \frac{-27}{31} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (x+4)& = & -8 \color{red}{-} (12+x) \\\Leftrightarrow & 3x+12& = &-8-12-x \\\Leftrightarrow & 3x \color{red}{+12} & = &-20 \color{red}{-x} \\\Leftrightarrow & 3x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-20 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 3x+x& = &-20-12 \\\Leftrightarrow & 4x& = &-32 \\\Leftrightarrow & \frac{4x}{ \color{red}{4} }& = &\frac{-32}{ \color{red}{4} } \\\Leftrightarrow & x = -8 & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (3x+2)& = & -6 \color{red}{-} (1+x) \\\Leftrightarrow & 12x+8& = &-6-1-x \\\Leftrightarrow & 12x \color{red}{+8} & = &-7 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & 12x+x& = &-7-8 \\\Leftrightarrow & 13x& = &-15 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-15}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-15}{13} & & \\ & V = \left\{ \frac{-15}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (2x+1)& = & -8 \color{red}{-} (15+x) \\\Leftrightarrow & 8x+4& = &-8-15-x \\\Leftrightarrow & 8x \color{red}{+4} & = &-23 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-23 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 8x+x& = &-23-4 \\\Leftrightarrow & 9x& = &-27 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-27}{ \color{red}{9} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (3x+4)& = & -7 \color{red}{-} (2+x) \\\Leftrightarrow & 18x+24& = &-7-2-x \\\Leftrightarrow & 18x \color{red}{+24} & = &-9 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 18x+x& = &-9-24 \\\Leftrightarrow & 19x& = &-33 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-33}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-33}{19} & & \\ & V = \left\{ \frac{-33}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-x+7)& = & -11 \color{red}{-} (9-3x) \\\Leftrightarrow & -4x+28& = &-11-9+3x \\\Leftrightarrow & -4x \color{red}{+28} & = &-20 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+28} \color{blue}{-28} \color{blue}{-3x} & = &-20 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-28} \\\Leftrightarrow & -4x-3x& = &-20-28 \\\Leftrightarrow & -7x& = &-48 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-48}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{48}{7} & & \\ & V = \left\{ \frac{48}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-6x+3)& = & -12 \color{red}{-} (12+x) \\\Leftrightarrow & -30x+15& = &-12-12-x \\\Leftrightarrow & -30x \color{red}{+15} & = &-24 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &-24 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & -30x+x& = &-24-15 \\\Leftrightarrow & -29x& = &-39 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-39}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{39}{29} & & \\ & V = \left\{ \frac{39}{29} \right\} & \\\end{align}\)