Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (3x-7)& = & -13 \color{red}{-} (2+x) \\\Leftrightarrow & 6x-14& = &-13-2-x \\\Leftrightarrow & 6x \color{red}{-14} & = &-15 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-14} \color{blue}{+14} \color{blue}{+x} & = &-15 \color{red}{-x} \color{blue}{+x} \color{blue}{+14} \\\Leftrightarrow & 6x+x& = &-15+14 \\\Leftrightarrow & 7x& = &-1 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-1}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-1}{7} & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-3x+6)& = & 1 \color{red}{-} (-11+x) \\\Leftrightarrow & -15x+30& = &1+11-x \\\Leftrightarrow & -15x \color{red}{+30} & = &12 \color{red}{-x} \\\Leftrightarrow & -15x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & -15x+x& = &12-30 \\\Leftrightarrow & -14x& = &-18 \\\Leftrightarrow & \frac{-14x}{ \color{red}{-14} }& = &\frac{-18}{ \color{red}{-14} } \\\Leftrightarrow & x = \frac{9}{7} & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (3x-5)& = & 8 \color{red}{+} (9+4x) \\\Leftrightarrow & 15x-25& = &8+9+4x \\\Leftrightarrow & 15x \color{red}{-25} & = &17 \color{red}{+4x} \\\Leftrightarrow & 15x \color{red}{-25} \color{blue}{+25} \color{blue}{-4x} & = &17 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+25} \\\Leftrightarrow & 15x-4x& = &17+25 \\\Leftrightarrow & 11x& = &42 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{42}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{42}{11} & & \\ & V = \left\{ \frac{42}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (4x+4)& = & -11 \color{red}{-} (2+x) \\\Leftrightarrow & 24x+24& = &-11-2-x \\\Leftrightarrow & 24x \color{red}{+24} & = &-13 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 24x+x& = &-13-24 \\\Leftrightarrow & 25x& = &-37 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-37}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-37}{25} & & \\ & V = \left\{ \frac{-37}{25} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (6x-6)& = & 13 \color{red}{-} (7+x) \\\Leftrightarrow & 30x-30& = &13-7-x \\\Leftrightarrow & 30x \color{red}{-30} & = &6 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 30x+x& = &6+30 \\\Leftrightarrow & 31x& = &36 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{36}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{36}{31} & & \\ & V = \left\{ \frac{36}{31} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (4x+5)& = & -7 \color{red}{+} (12-5x) \\\Leftrightarrow & 8x+10& = &-7+12-5x \\\Leftrightarrow & 8x \color{red}{+10} & = &5 \color{red}{-5x} \\\Leftrightarrow & 8x \color{red}{+10} \color{blue}{-10} \color{blue}{+5x} & = &5 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-10} \\\Leftrightarrow & 8x+5x& = &5-10 \\\Leftrightarrow & 13x& = &-5 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-5}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-5}{13} & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-2x-5)& = & 6 \color{red}{+} (-11+x) \\\Leftrightarrow & -12x-30& = &6-11+x \\\Leftrightarrow & -12x \color{red}{-30} & = &-5 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & -12x-x& = &-5+30 \\\Leftrightarrow & -13x& = &25 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{25}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-25}{13} & & \\ & V = \left\{ \frac{-25}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (4x+3)& = & 2 \color{red}{+} (-5+x) \\\Leftrightarrow & 24x+18& = &2-5+x \\\Leftrightarrow & 24x \color{red}{+18} & = &-3 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & 24x-x& = &-3-18 \\\Leftrightarrow & 23x& = &-21 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-21}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-21}{23} & & \\ & V = \left\{ \frac{-21}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (3x+2)& = & -4 \color{red}{-} (4+x) \\\Leftrightarrow & 9x+6& = &-4-4-x \\\Leftrightarrow & 9x \color{red}{+6} & = &-8 \color{red}{-x} \\\Leftrightarrow & 9x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 9x+x& = &-8-6 \\\Leftrightarrow & 10x& = &-14 \\\Leftrightarrow & \frac{10x}{ \color{red}{10} }& = &\frac{-14}{ \color{red}{10} } \\\Leftrightarrow & x = \frac{-7}{5} & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-2x-3)& = & 12 \color{red}{-} (-6-3x) \\\Leftrightarrow & -4x-6& = &12+6+3x \\\Leftrightarrow & -4x \color{red}{-6} & = &18 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-6} \color{blue}{+6} \color{blue}{-3x} & = &18 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+6} \\\Leftrightarrow & -4x-3x& = &18+6 \\\Leftrightarrow & -7x& = &24 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{24}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-24}{7} & & \\ & V = \left\{ \frac{-24}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (x+3)& = & 15 \color{red}{-} (14+x) \\\Leftrightarrow & 5x+15& = &15-14-x \\\Leftrightarrow & 5x \color{red}{+15} & = &1 \color{red}{-x} \\\Leftrightarrow & 5x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & 5x+x& = &1-15 \\\Leftrightarrow & 6x& = &-14 \\\Leftrightarrow & \frac{6x}{ \color{red}{6} }& = &\frac{-14}{ \color{red}{6} } \\\Leftrightarrow & x = \frac{-7}{3} & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (6x+3)& = & -7 \color{red}{-} (13+x) \\\Leftrightarrow & 30x+15& = &-7-13-x \\\Leftrightarrow & 30x \color{red}{+15} & = &-20 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &-20 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & 30x+x& = &-20-15 \\\Leftrightarrow & 31x& = &-35 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-35}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-35}{31} & & \\ & V = \left\{ \frac{-35}{31} \right\} & \\\end{align}\)