Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (2x+2)& = & 10 \color{red}{+} (6+x) \\\Leftrightarrow & 12x+12& = &10+6+x \\\Leftrightarrow & 12x \color{red}{+12} & = &16 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &16 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 12x-x& = &16-12 \\\Leftrightarrow & 11x& = &4 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{4}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{4}{11} & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-5x+6)& = & 14 \color{red}{-} (6+4x) \\\Leftrightarrow & -25x+30& = &14-6-4x \\\Leftrightarrow & -25x \color{red}{+30} & = &8 \color{red}{-4x} \\\Leftrightarrow & -25x \color{red}{+30} \color{blue}{-30} \color{blue}{+4x} & = &8 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-30} \\\Leftrightarrow & -25x+4x& = &8-30 \\\Leftrightarrow & -21x& = &-22 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-22}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{22}{21} & & \\ & V = \left\{ \frac{22}{21} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (x+7)& = & -11 \color{red}{+} (12-2x) \\\Leftrightarrow & 5x+35& = &-11+12-2x \\\Leftrightarrow & 5x \color{red}{+35} & = &1 \color{red}{-2x} \\\Leftrightarrow & 5x \color{red}{+35} \color{blue}{-35} \color{blue}{+2x} & = &1 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-35} \\\Leftrightarrow & 5x+2x& = &1-35 \\\Leftrightarrow & 7x& = &-34 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-34}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-34}{7} & & \\ & V = \left\{ \frac{-34}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-5x+3)& = & 14 \color{red}{+} (-11+x) \\\Leftrightarrow & -30x+18& = &14-11+x \\\Leftrightarrow & -30x \color{red}{+18} & = &3 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & -30x-x& = &3-18 \\\Leftrightarrow & -31x& = &-15 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-15}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{15}{31} & & \\ & V = \left\{ \frac{15}{31} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-2x+6)& = & 7 \color{red}{-} (-15+x) \\\Leftrightarrow & -12x+36& = &7+15-x \\\Leftrightarrow & -12x \color{red}{+36} & = &22 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &22 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & -12x+x& = &22-36 \\\Leftrightarrow & -11x& = &-14 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-14}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{14}{11} & & \\ & V = \left\{ \frac{14}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (3x+3)& = & -3 \color{red}{-} (4-2x) \\\Leftrightarrow & 15x+15& = &-3-4+2x \\\Leftrightarrow & 15x \color{red}{+15} & = &-7 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{+15} \color{blue}{-15} \color{blue}{-2x} & = &-7 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-15} \\\Leftrightarrow & 15x-2x& = &-7-15 \\\Leftrightarrow & 13x& = &-22 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-22}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-22}{13} & & \\ & V = \left\{ \frac{-22}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-3x-2)& = & 11 \color{red}{-} (-6+x) \\\Leftrightarrow & -18x-12& = &11+6-x \\\Leftrightarrow & -18x \color{red}{-12} & = &17 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &17 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -18x+x& = &17+12 \\\Leftrightarrow & -17x& = &29 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{29}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-29}{17} & & \\ & V = \left\{ \frac{-29}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-3x+7)& = & 2 \color{red}{+} (10+x) \\\Leftrightarrow & -6x+14& = &2+10+x \\\Leftrightarrow & -6x \color{red}{+14} & = &12 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+14} \color{blue}{-14} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{-14} \\\Leftrightarrow & -6x-x& = &12-14 \\\Leftrightarrow & -7x& = &-2 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-2}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{2}{7} & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (3x+7)& = & 10 \color{red}{-} (-4-2x) \\\Leftrightarrow & 15x+35& = &10+4+2x \\\Leftrightarrow & 15x \color{red}{+35} & = &14 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{+35} \color{blue}{-35} \color{blue}{-2x} & = &14 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-35} \\\Leftrightarrow & 15x-2x& = &14-35 \\\Leftrightarrow & 13x& = &-21 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-21}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-21}{13} & & \\ & V = \left\{ \frac{-21}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-6x+1)& = & 8 \color{red}{+} (14+x) \\\Leftrightarrow & -18x+3& = &8+14+x \\\Leftrightarrow & -18x \color{red}{+3} & = &22 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{+3} \color{blue}{-3} \color{blue}{-x} & = &22 \color{red}{+x} \color{blue}{-x} \color{blue}{-3} \\\Leftrightarrow & -18x-x& = &22-3 \\\Leftrightarrow & -19x& = &19 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{19}{ \color{red}{-19} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (5x-2)& = & -15 \color{red}{-} (-4+x) \\\Leftrightarrow & 20x-8& = &-15+4-x \\\Leftrightarrow & 20x \color{red}{-8} & = &-11 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 20x+x& = &-11+8 \\\Leftrightarrow & 21x& = &-3 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-3}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-1}{7} & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-6x-1)& = & -8 \color{red}{-} (-9+x) \\\Leftrightarrow & -24x-4& = &-8+9-x \\\Leftrightarrow & -24x \color{red}{-4} & = &1 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & -24x+x& = &1+4 \\\Leftrightarrow & -23x& = &5 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{5}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-5}{23} & & \\ & V = \left\{ \frac{-5}{23} \right\} & \\\end{align}\)