Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (2x-5)& = & -9 \color{red}{+} (8+x) \\\Leftrightarrow & 8x-20& = &-9+8+x \\\Leftrightarrow & 8x \color{red}{-20} & = &-1 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & 8x-x& = &-1+20 \\\Leftrightarrow & 7x& = &19 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{19}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{19}{7} & & \\ & V = \left\{ \frac{19}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (x+4)& = & 5 \color{red}{-} (-15-5x) \\\Leftrightarrow & 3x+12& = &5+15+5x \\\Leftrightarrow & 3x \color{red}{+12} & = &20 \color{red}{+5x} \\\Leftrightarrow & 3x \color{red}{+12} \color{blue}{-12} \color{blue}{-5x} & = &20 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-12} \\\Leftrightarrow & 3x-5x& = &20-12 \\\Leftrightarrow & -2x& = &8 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{8}{ \color{red}{-2} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (4x-2)& = & -1 \color{red}{+} (14+x) \\\Leftrightarrow & 20x-10& = &-1+14+x \\\Leftrightarrow & 20x \color{red}{-10} & = &13 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & 20x-x& = &13+10 \\\Leftrightarrow & 19x& = &23 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{23}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{23}{19} & & \\ & V = \left\{ \frac{23}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-5x+3)& = & 2 \color{red}{-} (-12+x) \\\Leftrightarrow & -30x+18& = &2+12-x \\\Leftrightarrow & -30x \color{red}{+18} & = &14 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & -30x+x& = &14-18 \\\Leftrightarrow & -29x& = &-4 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-4}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{4}{29} & & \\ & V = \left\{ \frac{4}{29} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (5x+4)& = & 11 \color{red}{+} (3+x) \\\Leftrightarrow & 15x+12& = &11+3+x \\\Leftrightarrow & 15x \color{red}{+12} & = &14 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &14 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 15x-x& = &14-12 \\\Leftrightarrow & 14x& = &2 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{2}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{1}{7} & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-x+6)& = & -6 \color{red}{+} (-9-3x) \\\Leftrightarrow & -4x+24& = &-6-9-3x \\\Leftrightarrow & -4x \color{red}{+24} & = &-15 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+24} \color{blue}{-24} \color{blue}{+3x} & = &-15 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-24} \\\Leftrightarrow & -4x+3x& = &-15-24 \\\Leftrightarrow & -x& = &-39 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-39}{ \color{red}{-1} } \\\Leftrightarrow & x = 39 & & \\ & V = \left\{ 39 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (2x+2)& = & 1 \color{red}{-} (13-3x) \\\Leftrightarrow & 10x+10& = &1-13+3x \\\Leftrightarrow & 10x \color{red}{+10} & = &-12 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+10} \color{blue}{-10} \color{blue}{-3x} & = &-12 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-10} \\\Leftrightarrow & 10x-3x& = &-12-10 \\\Leftrightarrow & 7x& = &-22 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-22}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-22}{7} & & \\ & V = \left\{ \frac{-22}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-5x-4)& = & -6 \color{red}{-} (12-2x) \\\Leftrightarrow & -15x-12& = &-6-12+2x \\\Leftrightarrow & -15x \color{red}{-12} & = &-18 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{-12} \color{blue}{+12} \color{blue}{-2x} & = &-18 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+12} \\\Leftrightarrow & -15x-2x& = &-18+12 \\\Leftrightarrow & -17x& = &-6 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-6}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{6}{17} & & \\ & V = \left\{ \frac{6}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (4x-5)& = & -14 \color{red}{+} (4+x) \\\Leftrightarrow & 24x-30& = &-14+4+x \\\Leftrightarrow & 24x \color{red}{-30} & = &-10 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 24x-x& = &-10+30 \\\Leftrightarrow & 23x& = &20 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{20}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{20}{23} & & \\ & V = \left\{ \frac{20}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-6x-3)& = & 12 \color{red}{+} (8-5x) \\\Leftrightarrow & -36x-18& = &12+8-5x \\\Leftrightarrow & -36x \color{red}{-18} & = &20 \color{red}{-5x} \\\Leftrightarrow & -36x \color{red}{-18} \color{blue}{+18} \color{blue}{+5x} & = &20 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+18} \\\Leftrightarrow & -36x+5x& = &20+18 \\\Leftrightarrow & -31x& = &38 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{38}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-38}{31} & & \\ & V = \left\{ \frac{-38}{31} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (x-4)& = & 14 \color{red}{-} (-14+2x) \\\Leftrightarrow & 5x-20& = &14+14-2x \\\Leftrightarrow & 5x \color{red}{-20} & = &28 \color{red}{-2x} \\\Leftrightarrow & 5x \color{red}{-20} \color{blue}{+20} \color{blue}{+2x} & = &28 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+20} \\\Leftrightarrow & 5x+2x& = &28+20 \\\Leftrightarrow & 7x& = &48 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{48}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{48}{7} & & \\ & V = \left\{ \frac{48}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (3x+7)& = & -4 \color{red}{-} (6-5x) \\\Leftrightarrow & 6x+14& = &-4-6+5x \\\Leftrightarrow & 6x \color{red}{+14} & = &-10 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+14} \color{blue}{-14} \color{blue}{-5x} & = &-10 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-14} \\\Leftrightarrow & 6x-5x& = &-10-14 \\\Leftrightarrow & x& = &-24 \\ & V = \left\{ -24 \right\} & \\\end{align}\)