Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (2x-1)& = & -15 \color{red}{-} (-1-3x) \\\Leftrightarrow & 4x-2& = &-15+1+3x \\\Leftrightarrow & 4x \color{red}{-2} & = &-14 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{-2} \color{blue}{+2} \color{blue}{-3x} & = &-14 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+2} \\\Leftrightarrow & 4x-3x& = &-14+2 \\\Leftrightarrow & x& = &-12 \\ & V = \left\{ -12 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (4x-6)& = & -12 \color{red}{-} (15+3x) \\\Leftrightarrow & 16x-24& = &-12-15-3x \\\Leftrightarrow & 16x \color{red}{-24} & = &-27 \color{red}{-3x} \\\Leftrightarrow & 16x \color{red}{-24} \color{blue}{+24} \color{blue}{+3x} & = &-27 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+24} \\\Leftrightarrow & 16x+3x& = &-27+24 \\\Leftrightarrow & 19x& = &-3 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-3}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-3}{19} & & \\ & V = \left\{ \frac{-3}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (4x+5)& = & 5 \color{red}{+} (-7+x) \\\Leftrightarrow & 20x+25& = &5-7+x \\\Leftrightarrow & 20x \color{red}{+25} & = &-2 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+25} \color{blue}{-25} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{-25} \\\Leftrightarrow & 20x-x& = &-2-25 \\\Leftrightarrow & 19x& = &-27 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-27}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-27}{19} & & \\ & V = \left\{ \frac{-27}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (3x+1)& = & 13 \color{red}{-} (-7-2x) \\\Leftrightarrow & 15x+5& = &13+7+2x \\\Leftrightarrow & 15x \color{red}{+5} & = &20 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{+5} \color{blue}{-5} \color{blue}{-2x} & = &20 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-5} \\\Leftrightarrow & 15x-2x& = &20-5 \\\Leftrightarrow & 13x& = &15 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{15}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{15}{13} & & \\ & V = \left\{ \frac{15}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-3x-3)& = & 5 \color{red}{-} (-9-5x) \\\Leftrightarrow & -18x-18& = &5+9+5x \\\Leftrightarrow & -18x \color{red}{-18} & = &14 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{-18} \color{blue}{+18} \color{blue}{-5x} & = &14 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+18} \\\Leftrightarrow & -18x-5x& = &14+18 \\\Leftrightarrow & -23x& = &32 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{32}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-32}{23} & & \\ & V = \left\{ \frac{-32}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (3x-6)& = & -1 \color{red}{+} (-5+x) \\\Leftrightarrow & 6x-12& = &-1-5+x \\\Leftrightarrow & 6x \color{red}{-12} & = &-6 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 6x-x& = &-6+12 \\\Leftrightarrow & 5x& = &6 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{6}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{6}{5} & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (2x-7)& = & -3 \color{red}{+} (5+3x) \\\Leftrightarrow & 10x-35& = &-3+5+3x \\\Leftrightarrow & 10x \color{red}{-35} & = &2 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{-35} \color{blue}{+35} \color{blue}{-3x} & = &2 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+35} \\\Leftrightarrow & 10x-3x& = &2+35 \\\Leftrightarrow & 7x& = &37 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{37}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{37}{7} & & \\ & V = \left\{ \frac{37}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-6x+5)& = & -7 \color{red}{+} (-8+x) \\\Leftrightarrow & -24x+20& = &-7-8+x \\\Leftrightarrow & -24x \color{red}{+20} & = &-15 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & -24x-x& = &-15-20 \\\Leftrightarrow & -25x& = &-35 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-35}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{7}{5} & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (x-2)& = & -8 \color{red}{+} (-11-3x) \\\Leftrightarrow & 4x-8& = &-8-11-3x \\\Leftrightarrow & 4x \color{red}{-8} & = &-19 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-8} \color{blue}{+8} \color{blue}{+3x} & = &-19 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+8} \\\Leftrightarrow & 4x+3x& = &-19+8 \\\Leftrightarrow & 7x& = &-11 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-11}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-11}{7} & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (5x+3)& = & -4 \color{red}{+} (4+x) \\\Leftrightarrow & 10x+6& = &-4+4+x \\\Leftrightarrow & 10x \color{red}{+6} & = &0 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 10x-x& = &0-6 \\\Leftrightarrow & 9x& = &-6 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-6}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-2}{3} & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (x+7)& = & 13 \color{red}{+} (14-5x) \\\Leftrightarrow & 6x+42& = &13+14-5x \\\Leftrightarrow & 6x \color{red}{+42} & = &27 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+42} \color{blue}{-42} \color{blue}{+5x} & = &27 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-42} \\\Leftrightarrow & 6x+5x& = &27-42 \\\Leftrightarrow & 11x& = &-15 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-15}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-15}{11} & & \\ & V = \left\{ \frac{-15}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-4x-6)& = & 10 \color{red}{-} (-6+x) \\\Leftrightarrow & -24x-36& = &10+6-x \\\Leftrightarrow & -24x \color{red}{-36} & = &16 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & -24x+x& = &16+36 \\\Leftrightarrow & -23x& = &52 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{52}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-52}{23} & & \\ & V = \left\{ \frac{-52}{23} \right\} & \\\end{align}\)