Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (4x+4)& = & 4 \color{red}{-} (-9-5x) \\\Leftrightarrow & 8x+8& = &4+9+5x \\\Leftrightarrow & 8x \color{red}{+8} & = &13 \color{red}{+5x} \\\Leftrightarrow & 8x \color{red}{+8} \color{blue}{-8} \color{blue}{-5x} & = &13 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-8} \\\Leftrightarrow & 8x-5x& = &13-8 \\\Leftrightarrow & 3x& = &5 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{5}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{5}{3} & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-6x+4)& = & 9 \color{red}{-} (15-5x) \\\Leftrightarrow & -36x+24& = &9-15+5x \\\Leftrightarrow & -36x \color{red}{+24} & = &-6 \color{red}{+5x} \\\Leftrightarrow & -36x \color{red}{+24} \color{blue}{-24} \color{blue}{-5x} & = &-6 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-24} \\\Leftrightarrow & -36x-5x& = &-6-24 \\\Leftrightarrow & -41x& = &-30 \\\Leftrightarrow & \frac{-41x}{ \color{red}{-41} }& = &\frac{-30}{ \color{red}{-41} } \\\Leftrightarrow & x = \frac{30}{41} & & \\ & V = \left\{ \frac{30}{41} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-4x+4)& = & -2 \color{red}{-} (-11+x) \\\Leftrightarrow & -24x+24& = &-2+11-x \\\Leftrightarrow & -24x \color{red}{+24} & = &9 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & -24x+x& = &9-24 \\\Leftrightarrow & -23x& = &-15 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-15}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{15}{23} & & \\ & V = \left\{ \frac{15}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (4x+3)& = & 5 \color{red}{-} (-12-5x) \\\Leftrightarrow & 8x+6& = &5+12+5x \\\Leftrightarrow & 8x \color{red}{+6} & = &17 \color{red}{+5x} \\\Leftrightarrow & 8x \color{red}{+6} \color{blue}{-6} \color{blue}{-5x} & = &17 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-6} \\\Leftrightarrow & 8x-5x& = &17-6 \\\Leftrightarrow & 3x& = &11 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{11}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{11}{3} & & \\ & V = \left\{ \frac{11}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-4x-3)& = & 9 \color{red}{-} (-3+x) \\\Leftrightarrow & -12x-9& = &9+3-x \\\Leftrightarrow & -12x \color{red}{-9} & = &12 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-9} \color{blue}{+9} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{+9} \\\Leftrightarrow & -12x+x& = &12+9 \\\Leftrightarrow & -11x& = &21 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{21}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-21}{11} & & \\ & V = \left\{ \frac{-21}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-3x-3)& = & -4 \color{red}{-} (-14+x) \\\Leftrightarrow & -12x-12& = &-4+14-x \\\Leftrightarrow & -12x \color{red}{-12} & = &10 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -12x+x& = &10+12 \\\Leftrightarrow & -11x& = &22 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{22}{ \color{red}{-11} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (3x-7)& = & 3 \color{red}{-} (-8+4x) \\\Leftrightarrow & 9x-21& = &3+8-4x \\\Leftrightarrow & 9x \color{red}{-21} & = &11 \color{red}{-4x} \\\Leftrightarrow & 9x \color{red}{-21} \color{blue}{+21} \color{blue}{+4x} & = &11 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+21} \\\Leftrightarrow & 9x+4x& = &11+21 \\\Leftrightarrow & 13x& = &32 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{32}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{32}{13} & & \\ & V = \left\{ \frac{32}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (x+7)& = & 6 \color{red}{-} (6-2x) \\\Leftrightarrow & 5x+35& = &6-6+2x \\\Leftrightarrow & 5x \color{red}{+35} & = &0 \color{red}{+2x} \\\Leftrightarrow & 5x \color{red}{+35} \color{blue}{-35} \color{blue}{-2x} & = &0 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-35} \\\Leftrightarrow & 5x-2x& = &0-35 \\\Leftrightarrow & 3x& = &-35 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-35}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-35}{3} & & \\ & V = \left\{ \frac{-35}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-3x+3)& = & -12 \color{red}{+} (2+x) \\\Leftrightarrow & -6x+6& = &-12+2+x \\\Leftrightarrow & -6x \color{red}{+6} & = &-10 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -6x-x& = &-10-6 \\\Leftrightarrow & -7x& = &-16 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-16}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{16}{7} & & \\ & V = \left\{ \frac{16}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (5x-6)& = & 7 \color{red}{+} (-3+x) \\\Leftrightarrow & 10x-12& = &7-3+x \\\Leftrightarrow & 10x \color{red}{-12} & = &4 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 10x-x& = &4+12 \\\Leftrightarrow & 9x& = &16 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{16}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{16}{9} & & \\ & V = \left\{ \frac{16}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (2x-5)& = & 14 \color{red}{+} (5-3x) \\\Leftrightarrow & 4x-10& = &14+5-3x \\\Leftrightarrow & 4x \color{red}{-10} & = &19 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-10} \color{blue}{+10} \color{blue}{+3x} & = &19 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+10} \\\Leftrightarrow & 4x+3x& = &19+10 \\\Leftrightarrow & 7x& = &29 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{29}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{29}{7} & & \\ & V = \left\{ \frac{29}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-x+1)& = & -15 \color{red}{+} (14-2x) \\\Leftrightarrow & -5x+5& = &-15+14-2x \\\Leftrightarrow & -5x \color{red}{+5} & = &-1 \color{red}{-2x} \\\Leftrightarrow & -5x \color{red}{+5} \color{blue}{-5} \color{blue}{+2x} & = &-1 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-5} \\\Leftrightarrow & -5x+2x& = &-1-5 \\\Leftrightarrow & -3x& = &-6 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-6}{ \color{red}{-3} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)