Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (5x+5)& = & -4 \color{red}{+} (15-3x) \\\Leftrightarrow & 10x+10& = &-4+15-3x \\\Leftrightarrow & 10x \color{red}{+10} & = &11 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+10} \color{blue}{-10} \color{blue}{+3x} & = &11 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-10} \\\Leftrightarrow & 10x+3x& = &11-10 \\\Leftrightarrow & 13x& = &1 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{1}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{1}{13} & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-5x+7)& = & -12 \color{red}{-} (-11-3x) \\\Leftrightarrow & -10x+14& = &-12+11+3x \\\Leftrightarrow & -10x \color{red}{+14} & = &-1 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{+14} \color{blue}{-14} \color{blue}{-3x} & = &-1 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-14} \\\Leftrightarrow & -10x-3x& = &-1-14 \\\Leftrightarrow & -13x& = &-15 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-15}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{15}{13} & & \\ & V = \left\{ \frac{15}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (2x-2)& = & 2 \color{red}{+} (-10-3x) \\\Leftrightarrow & 4x-4& = &2-10-3x \\\Leftrightarrow & 4x \color{red}{-4} & = &-8 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-4} \color{blue}{+4} \color{blue}{+3x} & = &-8 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+4} \\\Leftrightarrow & 4x+3x& = &-8+4 \\\Leftrightarrow & 7x& = &-4 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-4}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-4}{7} & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-6x+5)& = & 5 \color{red}{-} (12+x) \\\Leftrightarrow & -30x+25& = &5-12-x \\\Leftrightarrow & -30x \color{red}{+25} & = &-7 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+25} \color{blue}{-25} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{-25} \\\Leftrightarrow & -30x+x& = &-7-25 \\\Leftrightarrow & -29x& = &-32 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-32}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{32}{29} & & \\ & V = \left\{ \frac{32}{29} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-3x-4)& = & 6 \color{red}{+} (-15-2x) \\\Leftrightarrow & -15x-20& = &6-15-2x \\\Leftrightarrow & -15x \color{red}{-20} & = &-9 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{-20} \color{blue}{+20} \color{blue}{+2x} & = &-9 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+20} \\\Leftrightarrow & -15x+2x& = &-9+20 \\\Leftrightarrow & -13x& = &11 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{11}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-11}{13} & & \\ & V = \left\{ \frac{-11}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-4x+1)& = & 10 \color{red}{-} (1+x) \\\Leftrightarrow & -24x+6& = &10-1-x \\\Leftrightarrow & -24x \color{red}{+6} & = &9 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -24x+x& = &9-6 \\\Leftrightarrow & -23x& = &3 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{3}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-3}{23} & & \\ & V = \left\{ \frac{-3}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (5x+1)& = & 4 \color{red}{+} (-12+x) \\\Leftrightarrow & 15x+3& = &4-12+x \\\Leftrightarrow & 15x \color{red}{+3} & = &-8 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{+3} \color{blue}{-3} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{-3} \\\Leftrightarrow & 15x-x& = &-8-3 \\\Leftrightarrow & 14x& = &-11 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{-11}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{-11}{14} & & \\ & V = \left\{ \frac{-11}{14} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-6x+3)& = & -10 \color{red}{+} (14+x) \\\Leftrightarrow & -18x+9& = &-10+14+x \\\Leftrightarrow & -18x \color{red}{+9} & = &4 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{+9} \color{blue}{-9} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{-9} \\\Leftrightarrow & -18x-x& = &4-9 \\\Leftrightarrow & -19x& = &-5 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-5}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{5}{19} & & \\ & V = \left\{ \frac{5}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-2x-1)& = & 2 \color{red}{+} (8+x) \\\Leftrightarrow & -8x-4& = &2+8+x \\\Leftrightarrow & -8x \color{red}{-4} & = &10 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & -8x-x& = &10+4 \\\Leftrightarrow & -9x& = &14 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{14}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-14}{9} & & \\ & V = \left\{ \frac{-14}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (6x+4)& = & 12 \color{red}{-} (12+x) \\\Leftrightarrow & 36x+24& = &12-12-x \\\Leftrightarrow & 36x \color{red}{+24} & = &0 \color{red}{-x} \\\Leftrightarrow & 36x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 36x+x& = &0-24 \\\Leftrightarrow & 37x& = &-24 \\\Leftrightarrow & \frac{37x}{ \color{red}{37} }& = &\frac{-24}{ \color{red}{37} } \\\Leftrightarrow & x = \frac{-24}{37} & & \\ & V = \left\{ \frac{-24}{37} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-5x+6)& = & 6 \color{red}{-} (-2+x) \\\Leftrightarrow & -30x+36& = &6+2-x \\\Leftrightarrow & -30x \color{red}{+36} & = &8 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & -30x+x& = &8-36 \\\Leftrightarrow & -29x& = &-28 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-28}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{28}{29} & & \\ & V = \left\{ \frac{28}{29} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-2x-3)& = & 8 \color{red}{-} (-7+x) \\\Leftrightarrow & -8x-12& = &8+7-x \\\Leftrightarrow & -8x \color{red}{-12} & = &15 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &15 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -8x+x& = &15+12 \\\Leftrightarrow & -7x& = &27 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{27}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-27}{7} & & \\ & V = \left\{ \frac{-27}{7} \right\} & \\\end{align}\)