Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (5x-6)& = & -7 \color{red}{+} (10+x) \\\Leftrightarrow & 10x-12& = &-7+10+x \\\Leftrightarrow & 10x \color{red}{-12} & = &3 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 10x-x& = &3+12 \\\Leftrightarrow & 9x& = &15 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{15}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{5}{3} & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (3x+4)& = & 15 \color{red}{+} (-2+x) \\\Leftrightarrow & 18x+24& = &15-2+x \\\Leftrightarrow & 18x \color{red}{+24} & = &13 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 18x-x& = &13-24 \\\Leftrightarrow & 17x& = &-11 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-11}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-11}{17} & & \\ & V = \left\{ \frac{-11}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-3x-2)& = & 1 \color{red}{-} (14-4x) \\\Leftrightarrow & -9x-6& = &1-14+4x \\\Leftrightarrow & -9x \color{red}{-6} & = &-13 \color{red}{+4x} \\\Leftrightarrow & -9x \color{red}{-6} \color{blue}{+6} \color{blue}{-4x} & = &-13 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+6} \\\Leftrightarrow & -9x-4x& = &-13+6 \\\Leftrightarrow & -13x& = &-7 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-7}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{7}{13} & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (5x+5)& = & 12 \color{red}{-} (-6+x) \\\Leftrightarrow & 20x+20& = &12+6-x \\\Leftrightarrow & 20x \color{red}{+20} & = &18 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &18 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & 20x+x& = &18-20 \\\Leftrightarrow & 21x& = &-2 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-2}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-2}{21} & & \\ & V = \left\{ \frac{-2}{21} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-4x+5)& = & 15 \color{red}{-} (5+x) \\\Leftrightarrow & -8x+10& = &15-5-x \\\Leftrightarrow & -8x \color{red}{+10} & = &10 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & -8x+x& = &10-10 \\\Leftrightarrow & -7x& = &0 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{0}{ \color{red}{-7} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (5x+4)& = & 12 \color{red}{-} (-13+x) \\\Leftrightarrow & 10x+8& = &12+13-x \\\Leftrightarrow & 10x \color{red}{+8} & = &25 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &25 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & 10x+x& = &25-8 \\\Leftrightarrow & 11x& = &17 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{17}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{17}{11} & & \\ & V = \left\{ \frac{17}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-2x+4)& = & 7 \color{red}{+} (15+x) \\\Leftrightarrow & -8x+16& = &7+15+x \\\Leftrightarrow & -8x \color{red}{+16} & = &22 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{+16} \color{blue}{-16} \color{blue}{-x} & = &22 \color{red}{+x} \color{blue}{-x} \color{blue}{-16} \\\Leftrightarrow & -8x-x& = &22-16 \\\Leftrightarrow & -9x& = &6 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{6}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-2}{3} & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-4x+4)& = & -8 \color{red}{-} (1+x) \\\Leftrightarrow & -16x+16& = &-8-1-x \\\Leftrightarrow & -16x \color{red}{+16} & = &-9 \color{red}{-x} \\\Leftrightarrow & -16x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & -16x+x& = &-9-16 \\\Leftrightarrow & -15x& = &-25 \\\Leftrightarrow & \frac{-15x}{ \color{red}{-15} }& = &\frac{-25}{ \color{red}{-15} } \\\Leftrightarrow & x = \frac{5}{3} & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-6x-4)& = & 12 \color{red}{+} (-12-5x) \\\Leftrightarrow & -36x-24& = &12-12-5x \\\Leftrightarrow & -36x \color{red}{-24} & = &0 \color{red}{-5x} \\\Leftrightarrow & -36x \color{red}{-24} \color{blue}{+24} \color{blue}{+5x} & = &0 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+24} \\\Leftrightarrow & -36x+5x& = &0+24 \\\Leftrightarrow & -31x& = &24 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{24}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-24}{31} & & \\ & V = \left\{ \frac{-24}{31} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (3x+6)& = & 5 \color{red}{-} (-14+4x) \\\Leftrightarrow & 9x+18& = &5+14-4x \\\Leftrightarrow & 9x \color{red}{+18} & = &19 \color{red}{-4x} \\\Leftrightarrow & 9x \color{red}{+18} \color{blue}{-18} \color{blue}{+4x} & = &19 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-18} \\\Leftrightarrow & 9x+4x& = &19-18 \\\Leftrightarrow & 13x& = &1 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{1}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{1}{13} & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-6x-3)& = & -8 \color{red}{-} (-11-5x) \\\Leftrightarrow & -18x-9& = &-8+11+5x \\\Leftrightarrow & -18x \color{red}{-9} & = &3 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{-9} \color{blue}{+9} \color{blue}{-5x} & = &3 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+9} \\\Leftrightarrow & -18x-5x& = &3+9 \\\Leftrightarrow & -23x& = &12 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{12}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-12}{23} & & \\ & V = \left\{ \frac{-12}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (3x+3)& = & -1 \color{red}{+} (14-5x) \\\Leftrightarrow & 18x+18& = &-1+14-5x \\\Leftrightarrow & 18x \color{red}{+18} & = &13 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{+18} \color{blue}{-18} \color{blue}{+5x} & = &13 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-18} \\\Leftrightarrow & 18x+5x& = &13-18 \\\Leftrightarrow & 23x& = &-5 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-5}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-5}{23} & & \\ & V = \left\{ \frac{-5}{23} \right\} & \\\end{align}\)