Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (5x+1)& = & -5 \color{red}{+} (14-2x) \\\Leftrightarrow & 15x+3& = &-5+14-2x \\\Leftrightarrow & 15x \color{red}{+3} & = &9 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{+3} \color{blue}{-3} \color{blue}{+2x} & = &9 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-3} \\\Leftrightarrow & 15x+2x& = &9-3 \\\Leftrightarrow & 17x& = &6 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{6}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{6}{17} & & \\ & V = \left\{ \frac{6}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-3x+7)& = & -14 \color{red}{+} (-14-2x) \\\Leftrightarrow & -15x+35& = &-14-14-2x \\\Leftrightarrow & -15x \color{red}{+35} & = &-28 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{+35} \color{blue}{-35} \color{blue}{+2x} & = &-28 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-35} \\\Leftrightarrow & -15x+2x& = &-28-35 \\\Leftrightarrow & -13x& = &-63 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-63}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{63}{13} & & \\ & V = \left\{ \frac{63}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (3x+2)& = & 6 \color{red}{+} (-14+x) \\\Leftrightarrow & 15x+10& = &6-14+x \\\Leftrightarrow & 15x \color{red}{+10} & = &-8 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & 15x-x& = &-8-10 \\\Leftrightarrow & 14x& = &-18 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{-18}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{-9}{7} & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-6x+2)& = & 15 \color{red}{-} (-15+x) \\\Leftrightarrow & -24x+8& = &15+15-x \\\Leftrightarrow & -24x \color{red}{+8} & = &30 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &30 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & -24x+x& = &30-8 \\\Leftrightarrow & -23x& = &22 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{22}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-22}{23} & & \\ & V = \left\{ \frac{-22}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (6x-3)& = & 2 \color{red}{+} (3+x) \\\Leftrightarrow & 30x-15& = &2+3+x \\\Leftrightarrow & 30x \color{red}{-15} & = &5 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & 30x-x& = &5+15 \\\Leftrightarrow & 29x& = &20 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{20}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{20}{29} & & \\ & V = \left\{ \frac{20}{29} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-2x-5)& = & 9 \color{red}{-} (9-3x) \\\Leftrightarrow & -10x-25& = &9-9+3x \\\Leftrightarrow & -10x \color{red}{-25} & = &0 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{-25} \color{blue}{+25} \color{blue}{-3x} & = &0 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+25} \\\Leftrightarrow & -10x-3x& = &0+25 \\\Leftrightarrow & -13x& = &25 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{25}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-25}{13} & & \\ & V = \left\{ \frac{-25}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-6x+4)& = & 3 \color{red}{-} (-10+x) \\\Leftrightarrow & -36x+24& = &3+10-x \\\Leftrightarrow & -36x \color{red}{+24} & = &13 \color{red}{-x} \\\Leftrightarrow & -36x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & -36x+x& = &13-24 \\\Leftrightarrow & -35x& = &-11 \\\Leftrightarrow & \frac{-35x}{ \color{red}{-35} }& = &\frac{-11}{ \color{red}{-35} } \\\Leftrightarrow & x = \frac{11}{35} & & \\ & V = \left\{ \frac{11}{35} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (3x+7)& = & 8 \color{red}{-} (14-2x) \\\Leftrightarrow & 15x+35& = &8-14+2x \\\Leftrightarrow & 15x \color{red}{+35} & = &-6 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{+35} \color{blue}{-35} \color{blue}{-2x} & = &-6 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-35} \\\Leftrightarrow & 15x-2x& = &-6-35 \\\Leftrightarrow & 13x& = &-41 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-41}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-41}{13} & & \\ & V = \left\{ \frac{-41}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-5x+2)& = & 6 \color{red}{+} (14+x) \\\Leftrightarrow & -30x+12& = &6+14+x \\\Leftrightarrow & -30x \color{red}{+12} & = &20 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &20 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -30x-x& = &20-12 \\\Leftrightarrow & -31x& = &8 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{8}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-8}{31} & & \\ & V = \left\{ \frac{-8}{31} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (6x+4)& = & -7 \color{red}{+} (8+x) \\\Leftrightarrow & 24x+16& = &-7+8+x \\\Leftrightarrow & 24x \color{red}{+16} & = &1 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+16} \color{blue}{-16} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{-16} \\\Leftrightarrow & 24x-x& = &1-16 \\\Leftrightarrow & 23x& = &-15 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-15}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-15}{23} & & \\ & V = \left\{ \frac{-15}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (5x+2)& = & -10 \color{red}{-} (5+x) \\\Leftrightarrow & 20x+8& = &-10-5-x \\\Leftrightarrow & 20x \color{red}{+8} & = &-15 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &-15 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & 20x+x& = &-15-8 \\\Leftrightarrow & 21x& = &-23 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-23}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-23}{21} & & \\ & V = \left\{ \frac{-23}{21} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (3x-3)& = & -2 \color{red}{-} (-12-2x) \\\Leftrightarrow & 15x-15& = &-2+12+2x \\\Leftrightarrow & 15x \color{red}{-15} & = &10 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{-15} \color{blue}{+15} \color{blue}{-2x} & = &10 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+15} \\\Leftrightarrow & 15x-2x& = &10+15 \\\Leftrightarrow & 13x& = &25 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{25}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{25}{13} & & \\ & V = \left\{ \frac{25}{13} \right\} & \\\end{align}\)