Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (5x+7)& = & -13 \color{red}{-} (-5+3x) \\\Leftrightarrow & 20x+28& = &-13+5-3x \\\Leftrightarrow & 20x \color{red}{+28} & = &-8 \color{red}{-3x} \\\Leftrightarrow & 20x \color{red}{+28} \color{blue}{-28} \color{blue}{+3x} & = &-8 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-28} \\\Leftrightarrow & 20x+3x& = &-8-28 \\\Leftrightarrow & 23x& = &-36 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-36}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-36}{23} & & \\ & V = \left\{ \frac{-36}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (5x-2)& = & 8 \color{red}{-} (5-3x) \\\Leftrightarrow & 10x-4& = &8-5+3x \\\Leftrightarrow & 10x \color{red}{-4} & = &3 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{-4} \color{blue}{+4} \color{blue}{-3x} & = &3 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+4} \\\Leftrightarrow & 10x-3x& = &3+4 \\\Leftrightarrow & 7x& = &7 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{7}{ \color{red}{7} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (5x+3)& = & 6 \color{red}{-} (-14+x) \\\Leftrightarrow & 30x+18& = &6+14-x \\\Leftrightarrow & 30x \color{red}{+18} & = &20 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &20 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 30x+x& = &20-18 \\\Leftrightarrow & 31x& = &2 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{2}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{2}{31} & & \\ & V = \left\{ \frac{2}{31} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-6x+7)& = & -5 \color{red}{+} (4+x) \\\Leftrightarrow & -24x+28& = &-5+4+x \\\Leftrightarrow & -24x \color{red}{+28} & = &-1 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & -24x-x& = &-1-28 \\\Leftrightarrow & -25x& = &-29 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-29}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{29}{25} & & \\ & V = \left\{ \frac{29}{25} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-6x+2)& = & 1 \color{red}{+} (-5+x) \\\Leftrightarrow & -30x+10& = &1-5+x \\\Leftrightarrow & -30x \color{red}{+10} & = &-4 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & -30x-x& = &-4-10 \\\Leftrightarrow & -31x& = &-14 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-14}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{14}{31} & & \\ & V = \left\{ \frac{14}{31} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (6x+2)& = & 3 \color{red}{+} (10+x) \\\Leftrightarrow & 24x+8& = &3+10+x \\\Leftrightarrow & 24x \color{red}{+8} & = &13 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & 24x-x& = &13-8 \\\Leftrightarrow & 23x& = &5 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{5}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{5}{23} & & \\ & V = \left\{ \frac{5}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (6x-6)& = & 10 \color{red}{+} (13+x) \\\Leftrightarrow & 24x-24& = &10+13+x \\\Leftrightarrow & 24x \color{red}{-24} & = &23 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &23 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & 24x-x& = &23+24 \\\Leftrightarrow & 23x& = &47 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{47}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{47}{23} & & \\ & V = \left\{ \frac{47}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (x+4)& = & -2 \color{red}{+} (7+3x) \\\Leftrightarrow & 4x+16& = &-2+7+3x \\\Leftrightarrow & 4x \color{red}{+16} & = &5 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+16} \color{blue}{-16} \color{blue}{-3x} & = &5 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-16} \\\Leftrightarrow & 4x-3x& = &5-16 \\\Leftrightarrow & x& = &-11 \\ & V = \left\{ -11 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (x+3)& = & 6 \color{red}{-} (3-3x) \\\Leftrightarrow & 4x+12& = &6-3+3x \\\Leftrightarrow & 4x \color{red}{+12} & = &3 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+12} \color{blue}{-12} \color{blue}{-3x} & = &3 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-12} \\\Leftrightarrow & 4x-3x& = &3-12 \\\Leftrightarrow & x& = &-9 \\ & V = \left\{ -9 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (3x-5)& = & 2 \color{red}{+} (2-5x) \\\Leftrightarrow & 6x-10& = &2+2-5x \\\Leftrightarrow & 6x \color{red}{-10} & = &4 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{-10} \color{blue}{+10} \color{blue}{+5x} & = &4 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+10} \\\Leftrightarrow & 6x+5x& = &4+10 \\\Leftrightarrow & 11x& = &14 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{14}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{14}{11} & & \\ & V = \left\{ \frac{14}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (6x+5)& = & -6 \color{red}{-} (-4-5x) \\\Leftrightarrow & 18x+15& = &-6+4+5x \\\Leftrightarrow & 18x \color{red}{+15} & = &-2 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{+15} \color{blue}{-15} \color{blue}{-5x} & = &-2 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-15} \\\Leftrightarrow & 18x-5x& = &-2-15 \\\Leftrightarrow & 13x& = &-17 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-17}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-17}{13} & & \\ & V = \left\{ \frac{-17}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (4x+7)& = & 6 \color{red}{-} (5+x) \\\Leftrightarrow & 12x+21& = &6-5-x \\\Leftrightarrow & 12x \color{red}{+21} & = &1 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+21} \color{blue}{-21} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-21} \\\Leftrightarrow & 12x+x& = &1-21 \\\Leftrightarrow & 13x& = &-20 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-20}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-20}{13} & & \\ & V = \left\{ \frac{-20}{13} \right\} & \\\end{align}\)