Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-2x-1)& = & 8 \color{red}{-} (-15+x) \\\Leftrightarrow & -12x-6& = &8+15-x \\\Leftrightarrow & -12x \color{red}{-6} & = &23 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &23 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -12x+x& = &23+6 \\\Leftrightarrow & -11x& = &29 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{29}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-29}{11} & & \\ & V = \left\{ \frac{-29}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (4x+7)& = & 15 \color{red}{-} (14+x) \\\Leftrightarrow & 12x+21& = &15-14-x \\\Leftrightarrow & 12x \color{red}{+21} & = &1 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+21} \color{blue}{-21} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-21} \\\Leftrightarrow & 12x+x& = &1-21 \\\Leftrightarrow & 13x& = &-20 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-20}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-20}{13} & & \\ & V = \left\{ \frac{-20}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (5x+5)& = & 12 \color{red}{+} (10+x) \\\Leftrightarrow & 25x+25& = &12+10+x \\\Leftrightarrow & 25x \color{red}{+25} & = &22 \color{red}{+x} \\\Leftrightarrow & 25x \color{red}{+25} \color{blue}{-25} \color{blue}{-x} & = &22 \color{red}{+x} \color{blue}{-x} \color{blue}{-25} \\\Leftrightarrow & 25x-x& = &22-25 \\\Leftrightarrow & 24x& = &-3 \\\Leftrightarrow & \frac{24x}{ \color{red}{24} }& = &\frac{-3}{ \color{red}{24} } \\\Leftrightarrow & x = \frac{-1}{8} & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-2x-5)& = & 12 \color{red}{+} (3-3x) \\\Leftrightarrow & -4x-10& = &12+3-3x \\\Leftrightarrow & -4x \color{red}{-10} & = &15 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-10} \color{blue}{+10} \color{blue}{+3x} & = &15 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+10} \\\Leftrightarrow & -4x+3x& = &15+10 \\\Leftrightarrow & -x& = &25 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{25}{ \color{red}{-1} } \\\Leftrightarrow & x = -25 & & \\ & V = \left\{ -25 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (2x-7)& = & 11 \color{red}{-} (1+x) \\\Leftrightarrow & 12x-42& = &11-1-x \\\Leftrightarrow & 12x \color{red}{-42} & = &10 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & 12x+x& = &10+42 \\\Leftrightarrow & 13x& = &52 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{52}{ \color{red}{13} } \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (6x+1)& = & 6 \color{red}{+} (-5+x) \\\Leftrightarrow & 30x+5& = &6-5+x \\\Leftrightarrow & 30x \color{red}{+5} & = &1 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+5} \color{blue}{-5} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{-5} \\\Leftrightarrow & 30x-x& = &1-5 \\\Leftrightarrow & 29x& = &-4 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-4}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-4}{29} & & \\ & V = \left\{ \frac{-4}{29} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (x-4)& = & 11 \color{red}{-} (2-4x) \\\Leftrightarrow & 5x-20& = &11-2+4x \\\Leftrightarrow & 5x \color{red}{-20} & = &9 \color{red}{+4x} \\\Leftrightarrow & 5x \color{red}{-20} \color{blue}{+20} \color{blue}{-4x} & = &9 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+20} \\\Leftrightarrow & 5x-4x& = &9+20 \\\Leftrightarrow & x& = &29 \\ & V = \left\{ 29 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (3x-3)& = & -9 \color{red}{+} (5-2x) \\\Leftrightarrow & 15x-15& = &-9+5-2x \\\Leftrightarrow & 15x \color{red}{-15} & = &-4 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{-15} \color{blue}{+15} \color{blue}{+2x} & = &-4 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+15} \\\Leftrightarrow & 15x+2x& = &-4+15 \\\Leftrightarrow & 17x& = &11 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{11}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{11}{17} & & \\ & V = \left\{ \frac{11}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (x+5)& = & 11 \color{red}{+} (-6-2x) \\\Leftrightarrow & 5x+25& = &11-6-2x \\\Leftrightarrow & 5x \color{red}{+25} & = &5 \color{red}{-2x} \\\Leftrightarrow & 5x \color{red}{+25} \color{blue}{-25} \color{blue}{+2x} & = &5 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-25} \\\Leftrightarrow & 5x+2x& = &5-25 \\\Leftrightarrow & 7x& = &-20 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-20}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-20}{7} & & \\ & V = \left\{ \frac{-20}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (5x-2)& = & 13 \color{red}{-} (3+x) \\\Leftrightarrow & 30x-12& = &13-3-x \\\Leftrightarrow & 30x \color{red}{-12} & = &10 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 30x+x& = &10+12 \\\Leftrightarrow & 31x& = &22 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{22}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{22}{31} & & \\ & V = \left\{ \frac{22}{31} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (2x-2)& = & -12 \color{red}{-} (10+x) \\\Leftrightarrow & 8x-8& = &-12-10-x \\\Leftrightarrow & 8x \color{red}{-8} & = &-22 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &-22 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 8x+x& = &-22+8 \\\Leftrightarrow & 9x& = &-14 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-14}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-14}{9} & & \\ & V = \left\{ \frac{-14}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (4x-2)& = & 11 \color{red}{+} (1+x) \\\Leftrightarrow & 20x-10& = &11+1+x \\\Leftrightarrow & 20x \color{red}{-10} & = &12 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & 20x-x& = &12+10 \\\Leftrightarrow & 19x& = &22 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{22}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{22}{19} & & \\ & V = \left\{ \frac{22}{19} \right\} & \\\end{align}\)