Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-x+3)& = & -10 \color{red}{-} (11+4x) \\\Leftrightarrow & -5x+15& = &-10-11-4x \\\Leftrightarrow & -5x \color{red}{+15} & = &-21 \color{red}{-4x} \\\Leftrightarrow & -5x \color{red}{+15} \color{blue}{-15} \color{blue}{+4x} & = &-21 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-15} \\\Leftrightarrow & -5x+4x& = &-21-15 \\\Leftrightarrow & -x& = &-36 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-36}{ \color{red}{-1} } \\\Leftrightarrow & x = 36 & & \\ & V = \left\{ 36 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-2x-3)& = & 4 \color{red}{-} (11-5x) \\\Leftrightarrow & -6x-9& = &4-11+5x \\\Leftrightarrow & -6x \color{red}{-9} & = &-7 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-9} \color{blue}{+9} \color{blue}{-5x} & = &-7 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+9} \\\Leftrightarrow & -6x-5x& = &-7+9 \\\Leftrightarrow & -11x& = &2 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{2}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-2}{11} & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (4x-2)& = & -9 \color{red}{-} (-2+x) \\\Leftrightarrow & 8x-4& = &-9+2-x \\\Leftrightarrow & 8x \color{red}{-4} & = &-7 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & 8x+x& = &-7+4 \\\Leftrightarrow & 9x& = &-3 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-3}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-1}{3} & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (6x-7)& = & 9 \color{red}{+} (-8+x) \\\Leftrightarrow & 30x-35& = &9-8+x \\\Leftrightarrow & 30x \color{red}{-35} & = &1 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-35} \color{blue}{+35} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{+35} \\\Leftrightarrow & 30x-x& = &1+35 \\\Leftrightarrow & 29x& = &36 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{36}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{36}{29} & & \\ & V = \left\{ \frac{36}{29} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-4x+3)& = & 3 \color{red}{+} (-7+x) \\\Leftrightarrow & -20x+15& = &3-7+x \\\Leftrightarrow & -20x \color{red}{+15} & = &-4 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & -20x-x& = &-4-15 \\\Leftrightarrow & -21x& = &-19 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-19}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{19}{21} & & \\ & V = \left\{ \frac{19}{21} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (3x+3)& = & -15 \color{red}{-} (10+x) \\\Leftrightarrow & 15x+15& = &-15-10-x \\\Leftrightarrow & 15x \color{red}{+15} & = &-25 \color{red}{-x} \\\Leftrightarrow & 15x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &-25 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & 15x+x& = &-25-15 \\\Leftrightarrow & 16x& = &-40 \\\Leftrightarrow & \frac{16x}{ \color{red}{16} }& = &\frac{-40}{ \color{red}{16} } \\\Leftrightarrow & x = \frac{-5}{2} & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-5x-1)& = & -13 \color{red}{+} (-5+x) \\\Leftrightarrow & -30x-6& = &-13-5+x \\\Leftrightarrow & -30x \color{red}{-6} & = &-18 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-18 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -30x-x& = &-18+6 \\\Leftrightarrow & -31x& = &-12 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-12}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{12}{31} & & \\ & V = \left\{ \frac{12}{31} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (5x+6)& = & -11 \color{red}{-} (4-2x) \\\Leftrightarrow & 15x+18& = &-11-4+2x \\\Leftrightarrow & 15x \color{red}{+18} & = &-15 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{+18} \color{blue}{-18} \color{blue}{-2x} & = &-15 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-18} \\\Leftrightarrow & 15x-2x& = &-15-18 \\\Leftrightarrow & 13x& = &-33 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-33}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-33}{13} & & \\ & V = \left\{ \frac{-33}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (4x-6)& = & 5 \color{red}{+} (6+x) \\\Leftrightarrow & 24x-36& = &5+6+x \\\Leftrightarrow & 24x \color{red}{-36} & = &11 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-36} \color{blue}{+36} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{+36} \\\Leftrightarrow & 24x-x& = &11+36 \\\Leftrightarrow & 23x& = &47 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{47}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{47}{23} & & \\ & V = \left\{ \frac{47}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-3x-3)& = & -11 \color{red}{-} (11-2x) \\\Leftrightarrow & -15x-15& = &-11-11+2x \\\Leftrightarrow & -15x \color{red}{-15} & = &-22 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{-15} \color{blue}{+15} \color{blue}{-2x} & = &-22 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+15} \\\Leftrightarrow & -15x-2x& = &-22+15 \\\Leftrightarrow & -17x& = &-7 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-7}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{7}{17} & & \\ & V = \left\{ \frac{7}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (6x-5)& = & -8 \color{red}{+} (-14-5x) \\\Leftrightarrow & 18x-15& = &-8-14-5x \\\Leftrightarrow & 18x \color{red}{-15} & = &-22 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{-15} \color{blue}{+15} \color{blue}{+5x} & = &-22 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+15} \\\Leftrightarrow & 18x+5x& = &-22+15 \\\Leftrightarrow & 23x& = &-7 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-7}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-7}{23} & & \\ & V = \left\{ \frac{-7}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (x-3)& = & 10 \color{red}{-} (-5+4x) \\\Leftrightarrow & 5x-15& = &10+5-4x \\\Leftrightarrow & 5x \color{red}{-15} & = &15 \color{red}{-4x} \\\Leftrightarrow & 5x \color{red}{-15} \color{blue}{+15} \color{blue}{+4x} & = &15 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+15} \\\Leftrightarrow & 5x+4x& = &15+15 \\\Leftrightarrow & 9x& = &30 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{30}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{10}{3} & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)