Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (6x-4)& = & 4 \color{red}{-} (-4+x) \\\Leftrightarrow & 12x-8& = &4+4-x \\\Leftrightarrow & 12x \color{red}{-8} & = &8 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 12x+x& = &8+8 \\\Leftrightarrow & 13x& = &16 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{16}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{16}{13} & & \\ & V = \left\{ \frac{16}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (x+4)& = & -3 \color{red}{+} (-11+x) \\\Leftrightarrow & 2x+8& = &-3-11+x \\\Leftrightarrow & 2x \color{red}{+8} & = &-14 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & 2x-x& = &-14-8 \\\Leftrightarrow & x& = &-22 \\ & V = \left\{ -22 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (3x-5)& = & -14 \color{red}{-} (-7+x) \\\Leftrightarrow & 6x-10& = &-14+7-x \\\Leftrightarrow & 6x \color{red}{-10} & = &-7 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & 6x+x& = &-7+10 \\\Leftrightarrow & 7x& = &3 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{3}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{3}{7} & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (2x+2)& = & 9 \color{red}{-} (2-5x) \\\Leftrightarrow & 6x+6& = &9-2+5x \\\Leftrightarrow & 6x \color{red}{+6} & = &7 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+6} \color{blue}{-6} \color{blue}{-5x} & = &7 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-6} \\\Leftrightarrow & 6x-5x& = &7-6 \\\Leftrightarrow & x& = &1 \\ & V = \left\{ 1 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-4x+6)& = & 7 \color{red}{+} (-11+x) \\\Leftrightarrow & -24x+36& = &7-11+x \\\Leftrightarrow & -24x \color{red}{+36} & = &-4 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+36} \color{blue}{-36} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-36} \\\Leftrightarrow & -24x-x& = &-4-36 \\\Leftrightarrow & -25x& = &-40 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-40}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{8}{5} & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (x+5)& = & 10 \color{red}{-} (2-2x) \\\Leftrightarrow & 3x+15& = &10-2+2x \\\Leftrightarrow & 3x \color{red}{+15} & = &8 \color{red}{+2x} \\\Leftrightarrow & 3x \color{red}{+15} \color{blue}{-15} \color{blue}{-2x} & = &8 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-15} \\\Leftrightarrow & 3x-2x& = &8-15 \\\Leftrightarrow & x& = &-7 \\ & V = \left\{ -7 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (3x+7)& = & -3 \color{red}{-} (5+x) \\\Leftrightarrow & 12x+28& = &-3-5-x \\\Leftrightarrow & 12x \color{red}{+28} & = &-8 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+28} \color{blue}{-28} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{-28} \\\Leftrightarrow & 12x+x& = &-8-28 \\\Leftrightarrow & 13x& = &-36 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-36}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-36}{13} & & \\ & V = \left\{ \frac{-36}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-2x-5)& = & -10 \color{red}{-} (-9-3x) \\\Leftrightarrow & -4x-10& = &-10+9+3x \\\Leftrightarrow & -4x \color{red}{-10} & = &-1 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-10} \color{blue}{+10} \color{blue}{-3x} & = &-1 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+10} \\\Leftrightarrow & -4x-3x& = &-1+10 \\\Leftrightarrow & -7x& = &9 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{9}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-9}{7} & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (6x-6)& = & 11 \color{red}{+} (-3+x) \\\Leftrightarrow & 24x-24& = &11-3+x \\\Leftrightarrow & 24x \color{red}{-24} & = &8 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & 24x-x& = &8+24 \\\Leftrightarrow & 23x& = &32 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{32}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{32}{23} & & \\ & V = \left\{ \frac{32}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (5x-7)& = & 12 \color{red}{+} (7+x) \\\Leftrightarrow & 30x-42& = &12+7+x \\\Leftrightarrow & 30x \color{red}{-42} & = &19 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &19 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & 30x-x& = &19+42 \\\Leftrightarrow & 29x& = &61 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{61}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{61}{29} & & \\ & V = \left\{ \frac{61}{29} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (2x+3)& = & 5 \color{red}{+} (9-5x) \\\Leftrightarrow & 6x+9& = &5+9-5x \\\Leftrightarrow & 6x \color{red}{+9} & = &14 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+9} \color{blue}{-9} \color{blue}{+5x} & = &14 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-9} \\\Leftrightarrow & 6x+5x& = &14-9 \\\Leftrightarrow & 11x& = &5 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{5}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{5}{11} & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-4x+4)& = & -4 \color{red}{+} (7+x) \\\Leftrightarrow & -12x+12& = &-4+7+x \\\Leftrightarrow & -12x \color{red}{+12} & = &3 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -12x-x& = &3-12 \\\Leftrightarrow & -13x& = &-9 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-9}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{9}{13} & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)