Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (4x+3)& = & -1 \color{red}{-} (-12-5x) \\\Leftrightarrow & 16x+12& = &-1+12+5x \\\Leftrightarrow & 16x \color{red}{+12} & = &11 \color{red}{+5x} \\\Leftrightarrow & 16x \color{red}{+12} \color{blue}{-12} \color{blue}{-5x} & = &11 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-12} \\\Leftrightarrow & 16x-5x& = &11-12 \\\Leftrightarrow & 11x& = &-1 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-1}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-1}{11} & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-5x-5)& = & -13 \color{red}{+} (-3+x) \\\Leftrightarrow & -15x-15& = &-13-3+x \\\Leftrightarrow & -15x \color{red}{-15} & = &-16 \color{red}{+x} \\\Leftrightarrow & -15x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &-16 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & -15x-x& = &-16+15 \\\Leftrightarrow & -16x& = &-1 \\\Leftrightarrow & \frac{-16x}{ \color{red}{-16} }& = &\frac{-1}{ \color{red}{-16} } \\\Leftrightarrow & x = \frac{1}{16} & & \\ & V = \left\{ \frac{1}{16} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-2x-1)& = & 13 \color{red}{-} (9+3x) \\\Leftrightarrow & -10x-5& = &13-9-3x \\\Leftrightarrow & -10x \color{red}{-5} & = &4 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{-5} \color{blue}{+5} \color{blue}{+3x} & = &4 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+5} \\\Leftrightarrow & -10x+3x& = &4+5 \\\Leftrightarrow & -7x& = &9 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{9}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-9}{7} & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-x+1)& = & 4 \color{red}{+} (11-5x) \\\Leftrightarrow & -6x+6& = &4+11-5x \\\Leftrightarrow & -6x \color{red}{+6} & = &15 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{+6} \color{blue}{-6} \color{blue}{+5x} & = &15 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-6} \\\Leftrightarrow & -6x+5x& = &15-6 \\\Leftrightarrow & -x& = &9 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{9}{ \color{red}{-1} } \\\Leftrightarrow & x = -9 & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (5x+7)& = & -9 \color{red}{-} (1+3x) \\\Leftrightarrow & 20x+28& = &-9-1-3x \\\Leftrightarrow & 20x \color{red}{+28} & = &-10 \color{red}{-3x} \\\Leftrightarrow & 20x \color{red}{+28} \color{blue}{-28} \color{blue}{+3x} & = &-10 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-28} \\\Leftrightarrow & 20x+3x& = &-10-28 \\\Leftrightarrow & 23x& = &-38 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-38}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-38}{23} & & \\ & V = \left\{ \frac{-38}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (4x-6)& = & 15 \color{red}{-} (7+x) \\\Leftrightarrow & 16x-24& = &15-7-x \\\Leftrightarrow & 16x \color{red}{-24} & = &8 \color{red}{-x} \\\Leftrightarrow & 16x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 16x+x& = &8+24 \\\Leftrightarrow & 17x& = &32 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{32}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{32}{17} & & \\ & V = \left\{ \frac{32}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (x-1)& = & 8 \color{red}{+} (15+4x) \\\Leftrightarrow & 3x-3& = &8+15+4x \\\Leftrightarrow & 3x \color{red}{-3} & = &23 \color{red}{+4x} \\\Leftrightarrow & 3x \color{red}{-3} \color{blue}{+3} \color{blue}{-4x} & = &23 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+3} \\\Leftrightarrow & 3x-4x& = &23+3 \\\Leftrightarrow & -x& = &26 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{26}{ \color{red}{-1} } \\\Leftrightarrow & x = -26 & & \\ & V = \left\{ -26 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (3x-3)& = & 8 \color{red}{-} (-4+x) \\\Leftrightarrow & 6x-6& = &8+4-x \\\Leftrightarrow & 6x \color{red}{-6} & = &12 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 6x+x& = &12+6 \\\Leftrightarrow & 7x& = &18 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{18}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{18}{7} & & \\ & V = \left\{ \frac{18}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (2x+2)& = & -6 \color{red}{+} (4-5x) \\\Leftrightarrow & 6x+6& = &-6+4-5x \\\Leftrightarrow & 6x \color{red}{+6} & = &-2 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+6} \color{blue}{-6} \color{blue}{+5x} & = &-2 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-6} \\\Leftrightarrow & 6x+5x& = &-2-6 \\\Leftrightarrow & 11x& = &-8 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-8}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-8}{11} & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (4x-6)& = & -9 \color{red}{-} (-7+x) \\\Leftrightarrow & 12x-18& = &-9+7-x \\\Leftrightarrow & 12x \color{red}{-18} & = &-2 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & 12x+x& = &-2+18 \\\Leftrightarrow & 13x& = &16 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{16}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{16}{13} & & \\ & V = \left\{ \frac{16}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (5x-2)& = & 9 \color{red}{-} (-7+3x) \\\Leftrightarrow & 25x-10& = &9+7-3x \\\Leftrightarrow & 25x \color{red}{-10} & = &16 \color{red}{-3x} \\\Leftrightarrow & 25x \color{red}{-10} \color{blue}{+10} \color{blue}{+3x} & = &16 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+10} \\\Leftrightarrow & 25x+3x& = &16+10 \\\Leftrightarrow & 28x& = &26 \\\Leftrightarrow & \frac{28x}{ \color{red}{28} }& = &\frac{26}{ \color{red}{28} } \\\Leftrightarrow & x = \frac{13}{14} & & \\ & V = \left\{ \frac{13}{14} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (4x+6)& = & -8 \color{red}{-} (-11+x) \\\Leftrightarrow & 12x+18& = &-8+11-x \\\Leftrightarrow & 12x \color{red}{+18} & = &3 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 12x+x& = &3-18 \\\Leftrightarrow & 13x& = &-15 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-15}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-15}{13} & & \\ & V = \left\{ \frac{-15}{13} \right\} & \\\end{align}\)