Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-2x+5)& = & 9 \color{red}{-} (-13+x) \\\Leftrightarrow & -4x+10& = &9+13-x \\\Leftrightarrow & -4x \color{red}{+10} & = &22 \color{red}{-x} \\\Leftrightarrow & -4x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &22 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & -4x+x& = &22-10 \\\Leftrightarrow & -3x& = &12 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{12}{ \color{red}{-3} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-2x+5)& = & -4 \color{red}{+} (-14-3x) \\\Leftrightarrow & -10x+25& = &-4-14-3x \\\Leftrightarrow & -10x \color{red}{+25} & = &-18 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{+25} \color{blue}{-25} \color{blue}{+3x} & = &-18 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-25} \\\Leftrightarrow & -10x+3x& = &-18-25 \\\Leftrightarrow & -7x& = &-43 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-43}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{43}{7} & & \\ & V = \left\{ \frac{43}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (4x+6)& = & -7 \color{red}{+} (-7+x) \\\Leftrightarrow & 12x+18& = &-7-7+x \\\Leftrightarrow & 12x \color{red}{+18} & = &-14 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & 12x-x& = &-14-18 \\\Leftrightarrow & 11x& = &-32 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-32}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-32}{11} & & \\ & V = \left\{ \frac{-32}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (6x+3)& = & -4 \color{red}{+} (11-5x) \\\Leftrightarrow & 36x+18& = &-4+11-5x \\\Leftrightarrow & 36x \color{red}{+18} & = &7 \color{red}{-5x} \\\Leftrightarrow & 36x \color{red}{+18} \color{blue}{-18} \color{blue}{+5x} & = &7 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-18} \\\Leftrightarrow & 36x+5x& = &7-18 \\\Leftrightarrow & 41x& = &-11 \\\Leftrightarrow & \frac{41x}{ \color{red}{41} }& = &\frac{-11}{ \color{red}{41} } \\\Leftrightarrow & x = \frac{-11}{41} & & \\ & V = \left\{ \frac{-11}{41} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (3x+2)& = & 3 \color{red}{-} (-11+4x) \\\Leftrightarrow & 9x+6& = &3+11-4x \\\Leftrightarrow & 9x \color{red}{+6} & = &14 \color{red}{-4x} \\\Leftrightarrow & 9x \color{red}{+6} \color{blue}{-6} \color{blue}{+4x} & = &14 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-6} \\\Leftrightarrow & 9x+4x& = &14-6 \\\Leftrightarrow & 13x& = &8 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{8}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{8}{13} & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-2x-4)& = & 4 \color{red}{+} (11-5x) \\\Leftrightarrow & -6x-12& = &4+11-5x \\\Leftrightarrow & -6x \color{red}{-12} & = &15 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-12} \color{blue}{+12} \color{blue}{+5x} & = &15 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+12} \\\Leftrightarrow & -6x+5x& = &15+12 \\\Leftrightarrow & -x& = &27 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{27}{ \color{red}{-1} } \\\Leftrightarrow & x = -27 & & \\ & V = \left\{ -27 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (4x-1)& = & -10 \color{red}{+} (9+x) \\\Leftrightarrow & 20x-5& = &-10+9+x \\\Leftrightarrow & 20x \color{red}{-5} & = &-1 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-5} \color{blue}{+5} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{+5} \\\Leftrightarrow & 20x-x& = &-1+5 \\\Leftrightarrow & 19x& = &4 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{4}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{4}{19} & & \\ & V = \left\{ \frac{4}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (2x+6)& = & -1 \color{red}{-} (12+x) \\\Leftrightarrow & 8x+24& = &-1-12-x \\\Leftrightarrow & 8x \color{red}{+24} & = &-13 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 8x+x& = &-13-24 \\\Leftrightarrow & 9x& = &-37 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-37}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-37}{9} & & \\ & V = \left\{ \frac{-37}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-6x-3)& = & -13 \color{red}{-} (6-5x) \\\Leftrightarrow & -36x-18& = &-13-6+5x \\\Leftrightarrow & -36x \color{red}{-18} & = &-19 \color{red}{+5x} \\\Leftrightarrow & -36x \color{red}{-18} \color{blue}{+18} \color{blue}{-5x} & = &-19 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+18} \\\Leftrightarrow & -36x-5x& = &-19+18 \\\Leftrightarrow & -41x& = &-1 \\\Leftrightarrow & \frac{-41x}{ \color{red}{-41} }& = &\frac{-1}{ \color{red}{-41} } \\\Leftrightarrow & x = \frac{1}{41} & & \\ & V = \left\{ \frac{1}{41} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (6x+4)& = & 3 \color{red}{-} (-12+x) \\\Leftrightarrow & 12x+8& = &3+12-x \\\Leftrightarrow & 12x \color{red}{+8} & = &15 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &15 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & 12x+x& = &15-8 \\\Leftrightarrow & 13x& = &7 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{7}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{7}{13} & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-6x-1)& = & 12 \color{red}{+} (-14+x) \\\Leftrightarrow & -36x-6& = &12-14+x \\\Leftrightarrow & -36x \color{red}{-6} & = &-2 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -36x-x& = &-2+6 \\\Leftrightarrow & -37x& = &4 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{4}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{-4}{37} & & \\ & V = \left\{ \frac{-4}{37} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-4x+3)& = & 6 \color{red}{-} (-9+x) \\\Leftrightarrow & -12x+9& = &6+9-x \\\Leftrightarrow & -12x \color{red}{+9} & = &15 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+9} \color{blue}{-9} \color{blue}{+x} & = &15 \color{red}{-x} \color{blue}{+x} \color{blue}{-9} \\\Leftrightarrow & -12x+x& = &15-9 \\\Leftrightarrow & -11x& = &6 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{6}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-6}{11} & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)