Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (4x+1)& = & -2 \color{red}{-} (-10-5x) \\\Leftrightarrow & 16x+4& = &-2+10+5x \\\Leftrightarrow & 16x \color{red}{+4} & = &8 \color{red}{+5x} \\\Leftrightarrow & 16x \color{red}{+4} \color{blue}{-4} \color{blue}{-5x} & = &8 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-4} \\\Leftrightarrow & 16x-5x& = &8-4 \\\Leftrightarrow & 11x& = &4 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{4}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{4}{11} & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-2x-5)& = & 14 \color{red}{+} (15+x) \\\Leftrightarrow & -12x-30& = &14+15+x \\\Leftrightarrow & -12x \color{red}{-30} & = &29 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &29 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & -12x-x& = &29+30 \\\Leftrightarrow & -13x& = &59 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{59}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-59}{13} & & \\ & V = \left\{ \frac{-59}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (5x-3)& = & -6 \color{red}{+} (14+x) \\\Leftrightarrow & 20x-12& = &-6+14+x \\\Leftrightarrow & 20x \color{red}{-12} & = &8 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 20x-x& = &8+12 \\\Leftrightarrow & 19x& = &20 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{20}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{20}{19} & & \\ & V = \left\{ \frac{20}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-3x+7)& = & 15 \color{red}{+} (9+x) \\\Leftrightarrow & -12x+28& = &15+9+x \\\Leftrightarrow & -12x \color{red}{+28} & = &24 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &24 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & -12x-x& = &24-28 \\\Leftrightarrow & -13x& = &-4 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-4}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{4}{13} & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-4x-3)& = & -15 \color{red}{+} (13+x) \\\Leftrightarrow & -20x-15& = &-15+13+x \\\Leftrightarrow & -20x \color{red}{-15} & = &-2 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & -20x-x& = &-2+15 \\\Leftrightarrow & -21x& = &13 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{13}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-13}{21} & & \\ & V = \left\{ \frac{-13}{21} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-2x+7)& = & 12 \color{red}{+} (-6+3x) \\\Leftrightarrow & -8x+28& = &12-6+3x \\\Leftrightarrow & -8x \color{red}{+28} & = &6 \color{red}{+3x} \\\Leftrightarrow & -8x \color{red}{+28} \color{blue}{-28} \color{blue}{-3x} & = &6 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-28} \\\Leftrightarrow & -8x-3x& = &6-28 \\\Leftrightarrow & -11x& = &-22 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-22}{ \color{red}{-11} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (6x-6)& = & 4 \color{red}{+} (-7+x) \\\Leftrightarrow & 12x-12& = &4-7+x \\\Leftrightarrow & 12x \color{red}{-12} & = &-3 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 12x-x& = &-3+12 \\\Leftrightarrow & 11x& = &9 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{9}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{9}{11} & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-2x+4)& = & -14 \color{red}{-} (12-3x) \\\Leftrightarrow & -10x+20& = &-14-12+3x \\\Leftrightarrow & -10x \color{red}{+20} & = &-26 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{+20} \color{blue}{-20} \color{blue}{-3x} & = &-26 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-20} \\\Leftrightarrow & -10x-3x& = &-26-20 \\\Leftrightarrow & -13x& = &-46 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-46}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{46}{13} & & \\ & V = \left\{ \frac{46}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-4x-3)& = & -11 \color{red}{-} (8+x) \\\Leftrightarrow & -12x-9& = &-11-8-x \\\Leftrightarrow & -12x \color{red}{-9} & = &-19 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-9} \color{blue}{+9} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{+9} \\\Leftrightarrow & -12x+x& = &-19+9 \\\Leftrightarrow & -11x& = &-10 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-10}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{10}{11} & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (6x+4)& = & -11 \color{red}{+} (-3+x) \\\Leftrightarrow & 12x+8& = &-11-3+x \\\Leftrightarrow & 12x \color{red}{+8} & = &-14 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & 12x-x& = &-14-8 \\\Leftrightarrow & 11x& = &-22 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-22}{ \color{red}{11} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-6x+2)& = & -8 \color{red}{-} (11+x) \\\Leftrightarrow & -30x+10& = &-8-11-x \\\Leftrightarrow & -30x \color{red}{+10} & = &-19 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & -30x+x& = &-19-10 \\\Leftrightarrow & -29x& = &-29 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-29}{ \color{red}{-29} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (6x+6)& = & -6 \color{red}{+} (-8+x) \\\Leftrightarrow & 12x+12& = &-6-8+x \\\Leftrightarrow & 12x \color{red}{+12} & = &-14 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 12x-x& = &-14-12 \\\Leftrightarrow & 11x& = &-26 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-26}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-26}{11} & & \\ & V = \left\{ \frac{-26}{11} \right\} & \\\end{align}\)