Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (6x+4)& = & -14 \color{red}{+} (-13+x) \\\Leftrightarrow & 12x+8& = &-14-13+x \\\Leftrightarrow & 12x \color{red}{+8} & = &-27 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &-27 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & 12x-x& = &-27-8 \\\Leftrightarrow & 11x& = &-35 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-35}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-35}{11} & & \\ & V = \left\{ \frac{-35}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (5x-3)& = & 1 \color{red}{-} (9+x) \\\Leftrightarrow & 20x-12& = &1-9-x \\\Leftrightarrow & 20x \color{red}{-12} & = &-8 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 20x+x& = &-8+12 \\\Leftrightarrow & 21x& = &4 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{4}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{4}{21} & & \\ & V = \left\{ \frac{4}{21} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (5x-5)& = & 15 \color{red}{-} (6-3x) \\\Leftrightarrow & 10x-10& = &15-6+3x \\\Leftrightarrow & 10x \color{red}{-10} & = &9 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{-10} \color{blue}{+10} \color{blue}{-3x} & = &9 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+10} \\\Leftrightarrow & 10x-3x& = &9+10 \\\Leftrightarrow & 7x& = &19 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{19}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{19}{7} & & \\ & V = \left\{ \frac{19}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (x-7)& = & -10 \color{red}{-} (12+x) \\\Leftrightarrow & 6x-42& = &-10-12-x \\\Leftrightarrow & 6x \color{red}{-42} & = &-22 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &-22 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & 6x+x& = &-22+42 \\\Leftrightarrow & 7x& = &20 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{20}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{20}{7} & & \\ & V = \left\{ \frac{20}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-4x+5)& = & 11 \color{red}{-} (-1-5x) \\\Leftrightarrow & -8x+10& = &11+1+5x \\\Leftrightarrow & -8x \color{red}{+10} & = &12 \color{red}{+5x} \\\Leftrightarrow & -8x \color{red}{+10} \color{blue}{-10} \color{blue}{-5x} & = &12 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-10} \\\Leftrightarrow & -8x-5x& = &12-10 \\\Leftrightarrow & -13x& = &2 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{2}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-2}{13} & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-2x+1)& = & 5 \color{red}{+} (-1-3x) \\\Leftrightarrow & -4x+2& = &5-1-3x \\\Leftrightarrow & -4x \color{red}{+2} & = &4 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+2} \color{blue}{-2} \color{blue}{+3x} & = &4 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-2} \\\Leftrightarrow & -4x+3x& = &4-2 \\\Leftrightarrow & -x& = &2 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{2}{ \color{red}{-1} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (6x-1)& = & 12 \color{red}{-} (1+x) \\\Leftrightarrow & 36x-6& = &12-1-x \\\Leftrightarrow & 36x \color{red}{-6} & = &11 \color{red}{-x} \\\Leftrightarrow & 36x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 36x+x& = &11+6 \\\Leftrightarrow & 37x& = &17 \\\Leftrightarrow & \frac{37x}{ \color{red}{37} }& = &\frac{17}{ \color{red}{37} } \\\Leftrightarrow & x = \frac{17}{37} & & \\ & V = \left\{ \frac{17}{37} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-3x-7)& = & 13 \color{red}{-} (-4+4x) \\\Leftrightarrow & -15x-35& = &13+4-4x \\\Leftrightarrow & -15x \color{red}{-35} & = &17 \color{red}{-4x} \\\Leftrightarrow & -15x \color{red}{-35} \color{blue}{+35} \color{blue}{+4x} & = &17 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+35} \\\Leftrightarrow & -15x+4x& = &17+35 \\\Leftrightarrow & -11x& = &52 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{52}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-52}{11} & & \\ & V = \left\{ \frac{-52}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (3x-7)& = & 15 \color{red}{+} (14+x) \\\Leftrightarrow & 9x-21& = &15+14+x \\\Leftrightarrow & 9x \color{red}{-21} & = &29 \color{red}{+x} \\\Leftrightarrow & 9x \color{red}{-21} \color{blue}{+21} \color{blue}{-x} & = &29 \color{red}{+x} \color{blue}{-x} \color{blue}{+21} \\\Leftrightarrow & 9x-x& = &29+21 \\\Leftrightarrow & 8x& = &50 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{50}{ \color{red}{8} } \\\Leftrightarrow & x = \frac{25}{4} & & \\ & V = \left\{ \frac{25}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (6x-6)& = & -4 \color{red}{+} (-2-5x) \\\Leftrightarrow & 18x-18& = &-4-2-5x \\\Leftrightarrow & 18x \color{red}{-18} & = &-6 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{-18} \color{blue}{+18} \color{blue}{+5x} & = &-6 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+18} \\\Leftrightarrow & 18x+5x& = &-6+18 \\\Leftrightarrow & 23x& = &12 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{12}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{12}{23} & & \\ & V = \left\{ \frac{12}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (5x-1)& = & 2 \color{red}{+} (10+x) \\\Leftrightarrow & 30x-6& = &2+10+x \\\Leftrightarrow & 30x \color{red}{-6} & = &12 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 30x-x& = &12+6 \\\Leftrightarrow & 29x& = &18 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{18}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{18}{29} & & \\ & V = \left\{ \frac{18}{29} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (4x-2)& = & 8 \color{red}{+} (-15+x) \\\Leftrightarrow & 24x-12& = &8-15+x \\\Leftrightarrow & 24x \color{red}{-12} & = &-7 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 24x-x& = &-7+12 \\\Leftrightarrow & 23x& = &5 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{5}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{5}{23} & & \\ & V = \left\{ \frac{5}{23} \right\} & \\\end{align}\)