Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-6x-1)& = & -6 \color{red}{+} (8-5x) \\\Leftrightarrow & -18x-3& = &-6+8-5x \\\Leftrightarrow & -18x \color{red}{-3} & = &2 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{-3} \color{blue}{+3} \color{blue}{+5x} & = &2 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+3} \\\Leftrightarrow & -18x+5x& = &2+3 \\\Leftrightarrow & -13x& = &5 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{5}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-5}{13} & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-4x+7)& = & -4 \color{red}{+} (-3+x) \\\Leftrightarrow & -24x+42& = &-4-3+x \\\Leftrightarrow & -24x \color{red}{+42} & = &-7 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & -24x-x& = &-7-42 \\\Leftrightarrow & -25x& = &-49 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-49}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{49}{25} & & \\ & V = \left\{ \frac{49}{25} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (x-3)& = & 15 \color{red}{-} (7+x) \\\Leftrightarrow & 5x-15& = &15-7-x \\\Leftrightarrow & 5x \color{red}{-15} & = &8 \color{red}{-x} \\\Leftrightarrow & 5x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & 5x+x& = &8+15 \\\Leftrightarrow & 6x& = &23 \\\Leftrightarrow & \frac{6x}{ \color{red}{6} }& = &\frac{23}{ \color{red}{6} } \\\Leftrightarrow & x = \frac{23}{6} & & \\ & V = \left\{ \frac{23}{6} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (4x+3)& = & 11 \color{red}{-} (-11+x) \\\Leftrightarrow & 24x+18& = &11+11-x \\\Leftrightarrow & 24x \color{red}{+18} & = &22 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &22 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 24x+x& = &22-18 \\\Leftrightarrow & 25x& = &4 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{4}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{4}{25} & & \\ & V = \left\{ \frac{4}{25} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (2x-2)& = & 15 \color{red}{-} (6-3x) \\\Leftrightarrow & 4x-4& = &15-6+3x \\\Leftrightarrow & 4x \color{red}{-4} & = &9 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{-4} \color{blue}{+4} \color{blue}{-3x} & = &9 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+4} \\\Leftrightarrow & 4x-3x& = &9+4 \\\Leftrightarrow & x& = &13 \\ & V = \left\{ 13 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-x+3)& = & 11 \color{red}{-} (-4-5x) \\\Leftrightarrow & -3x+9& = &11+4+5x \\\Leftrightarrow & -3x \color{red}{+9} & = &15 \color{red}{+5x} \\\Leftrightarrow & -3x \color{red}{+9} \color{blue}{-9} \color{blue}{-5x} & = &15 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-9} \\\Leftrightarrow & -3x-5x& = &15-9 \\\Leftrightarrow & -8x& = &6 \\\Leftrightarrow & \frac{-8x}{ \color{red}{-8} }& = &\frac{6}{ \color{red}{-8} } \\\Leftrightarrow & x = \frac{-3}{4} & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (2x-1)& = & -7 \color{red}{-} (-15-3x) \\\Leftrightarrow & 10x-5& = &-7+15+3x \\\Leftrightarrow & 10x \color{red}{-5} & = &8 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{-5} \color{blue}{+5} \color{blue}{-3x} & = &8 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+5} \\\Leftrightarrow & 10x-3x& = &8+5 \\\Leftrightarrow & 7x& = &13 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{13}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{13}{7} & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (2x+4)& = & 14 \color{red}{+} (-7+x) \\\Leftrightarrow & 4x+8& = &14-7+x \\\Leftrightarrow & 4x \color{red}{+8} & = &7 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & 4x-x& = &7-8 \\\Leftrightarrow & 3x& = &-1 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-1}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-1}{3} & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-4x+2)& = & -8 \color{red}{-} (-12+x) \\\Leftrightarrow & -20x+10& = &-8+12-x \\\Leftrightarrow & -20x \color{red}{+10} & = &4 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & -20x+x& = &4-10 \\\Leftrightarrow & -19x& = &-6 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-6}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{6}{19} & & \\ & V = \left\{ \frac{6}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (x+1)& = & 5 \color{red}{-} (10+x) \\\Leftrightarrow & 3x+3& = &5-10-x \\\Leftrightarrow & 3x \color{red}{+3} & = &-5 \color{red}{-x} \\\Leftrightarrow & 3x \color{red}{+3} \color{blue}{-3} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{-3} \\\Leftrightarrow & 3x+x& = &-5-3 \\\Leftrightarrow & 4x& = &-8 \\\Leftrightarrow & \frac{4x}{ \color{red}{4} }& = &\frac{-8}{ \color{red}{4} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (2x-2)& = & 7 \color{red}{+} (4+x) \\\Leftrightarrow & 10x-10& = &7+4+x \\\Leftrightarrow & 10x \color{red}{-10} & = &11 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & 10x-x& = &11+10 \\\Leftrightarrow & 9x& = &21 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{21}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{7}{3} & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-6x+5)& = & 1 \color{red}{+} (-3+x) \\\Leftrightarrow & -30x+25& = &1-3+x \\\Leftrightarrow & -30x \color{red}{+25} & = &-2 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+25} \color{blue}{-25} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{-25} \\\Leftrightarrow & -30x-x& = &-2-25 \\\Leftrightarrow & -31x& = &-27 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-27}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{27}{31} & & \\ & V = \left\{ \frac{27}{31} \right\} & \\\end{align}\)