Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-2x+4)& = & 12 \color{red}{-} (14-3x) \\\Leftrightarrow & -4x+8& = &12-14+3x \\\Leftrightarrow & -4x \color{red}{+8} & = &-2 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+8} \color{blue}{-8} \color{blue}{-3x} & = &-2 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-8} \\\Leftrightarrow & -4x-3x& = &-2-8 \\\Leftrightarrow & -7x& = &-10 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-10}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{10}{7} & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-3x+2)& = & 15 \color{red}{-} (-2+x) \\\Leftrightarrow & -12x+8& = &15+2-x \\\Leftrightarrow & -12x \color{red}{+8} & = &17 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &17 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & -12x+x& = &17-8 \\\Leftrightarrow & -11x& = &9 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{9}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-9}{11} & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (4x-2)& = & 9 \color{red}{-} (-7+x) \\\Leftrightarrow & 12x-6& = &9+7-x \\\Leftrightarrow & 12x \color{red}{-6} & = &16 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 12x+x& = &16+6 \\\Leftrightarrow & 13x& = &22 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{22}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{22}{13} & & \\ & V = \left\{ \frac{22}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-4x-1)& = & -2 \color{red}{-} (7+x) \\\Leftrightarrow & -24x-6& = &-2-7-x \\\Leftrightarrow & -24x \color{red}{-6} & = &-9 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -24x+x& = &-9+6 \\\Leftrightarrow & -23x& = &-3 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-3}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{3}{23} & & \\ & V = \left\{ \frac{3}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-6x-4)& = & 5 \color{red}{+} (7+x) \\\Leftrightarrow & -12x-8& = &5+7+x \\\Leftrightarrow & -12x \color{red}{-8} & = &12 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & -12x-x& = &12+8 \\\Leftrightarrow & -13x& = &20 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{20}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-20}{13} & & \\ & V = \left\{ \frac{-20}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (x+2)& = & 12 \color{red}{-} (9+x) \\\Leftrightarrow & 2x+4& = &12-9-x \\\Leftrightarrow & 2x \color{red}{+4} & = &3 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 2x+x& = &3-4 \\\Leftrightarrow & 3x& = &-1 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-1}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-1}{3} & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-3x+4)& = & -12 \color{red}{+} (-1-5x) \\\Leftrightarrow & -18x+24& = &-12-1-5x \\\Leftrightarrow & -18x \color{red}{+24} & = &-13 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{+24} \color{blue}{-24} \color{blue}{+5x} & = &-13 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-24} \\\Leftrightarrow & -18x+5x& = &-13-24 \\\Leftrightarrow & -13x& = &-37 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-37}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{37}{13} & & \\ & V = \left\{ \frac{37}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (6x+1)& = & 13 \color{red}{+} (1+x) \\\Leftrightarrow & 18x+3& = &13+1+x \\\Leftrightarrow & 18x \color{red}{+3} & = &14 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{+3} \color{blue}{-3} \color{blue}{-x} & = &14 \color{red}{+x} \color{blue}{-x} \color{blue}{-3} \\\Leftrightarrow & 18x-x& = &14-3 \\\Leftrightarrow & 17x& = &11 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{11}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{11}{17} & & \\ & V = \left\{ \frac{11}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-5x+3)& = & 10 \color{red}{+} (12+x) \\\Leftrightarrow & -15x+9& = &10+12+x \\\Leftrightarrow & -15x \color{red}{+9} & = &22 \color{red}{+x} \\\Leftrightarrow & -15x \color{red}{+9} \color{blue}{-9} \color{blue}{-x} & = &22 \color{red}{+x} \color{blue}{-x} \color{blue}{-9} \\\Leftrightarrow & -15x-x& = &22-9 \\\Leftrightarrow & -16x& = &13 \\\Leftrightarrow & \frac{-16x}{ \color{red}{-16} }& = &\frac{13}{ \color{red}{-16} } \\\Leftrightarrow & x = \frac{-13}{16} & & \\ & V = \left\{ \frac{-13}{16} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-6x+5)& = & 3 \color{red}{+} (-12-5x) \\\Leftrightarrow & -18x+15& = &3-12-5x \\\Leftrightarrow & -18x \color{red}{+15} & = &-9 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{+15} \color{blue}{-15} \color{blue}{+5x} & = &-9 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-15} \\\Leftrightarrow & -18x+5x& = &-9-15 \\\Leftrightarrow & -13x& = &-24 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-24}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{24}{13} & & \\ & V = \left\{ \frac{24}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-5x+5)& = & -9 \color{red}{-} (-10+x) \\\Leftrightarrow & -30x+30& = &-9+10-x \\\Leftrightarrow & -30x \color{red}{+30} & = &1 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & -30x+x& = &1-30 \\\Leftrightarrow & -29x& = &-29 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-29}{ \color{red}{-29} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (4x+5)& = & 7 \color{red}{+} (-9+x) \\\Leftrightarrow & 20x+25& = &7-9+x \\\Leftrightarrow & 20x \color{red}{+25} & = &-2 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+25} \color{blue}{-25} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{-25} \\\Leftrightarrow & 20x-x& = &-2-25 \\\Leftrightarrow & 19x& = &-27 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-27}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-27}{19} & & \\ & V = \left\{ \frac{-27}{19} \right\} & \\\end{align}\)