Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (x-1)& = & 2 \color{red}{+} (3-2x) \\\Leftrightarrow & 3x-3& = &2+3-2x \\\Leftrightarrow & 3x \color{red}{-3} & = &5 \color{red}{-2x} \\\Leftrightarrow & 3x \color{red}{-3} \color{blue}{+3} \color{blue}{+2x} & = &5 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+3} \\\Leftrightarrow & 3x+2x& = &5+3 \\\Leftrightarrow & 5x& = &8 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{8}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{8}{5} & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (x-4)& = & -2 \color{red}{+} (9-3x) \\\Leftrightarrow & 4x-16& = &-2+9-3x \\\Leftrightarrow & 4x \color{red}{-16} & = &7 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-16} \color{blue}{+16} \color{blue}{+3x} & = &7 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+16} \\\Leftrightarrow & 4x+3x& = &7+16 \\\Leftrightarrow & 7x& = &23 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{23}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{23}{7} & & \\ & V = \left\{ \frac{23}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-x-7)& = & -10 \color{red}{+} (9+x) \\\Leftrightarrow & -2x-14& = &-10+9+x \\\Leftrightarrow & -2x \color{red}{-14} & = &-1 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{-14} \color{blue}{+14} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{+14} \\\Leftrightarrow & -2x-x& = &-1+14 \\\Leftrightarrow & -3x& = &13 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{13}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{-13}{3} & & \\ & V = \left\{ \frac{-13}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-5x-7)& = & 10 \color{red}{-} (3+x) \\\Leftrightarrow & -30x-42& = &10-3-x \\\Leftrightarrow & -30x \color{red}{-42} & = &7 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & -30x+x& = &7+42 \\\Leftrightarrow & -29x& = &49 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{49}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-49}{29} & & \\ & V = \left\{ \frac{-49}{29} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-3x-5)& = & 11 \color{red}{+} (14-5x) \\\Leftrightarrow & -6x-10& = &11+14-5x \\\Leftrightarrow & -6x \color{red}{-10} & = &25 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-10} \color{blue}{+10} \color{blue}{+5x} & = &25 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+10} \\\Leftrightarrow & -6x+5x& = &25+10 \\\Leftrightarrow & -x& = &35 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{35}{ \color{red}{-1} } \\\Leftrightarrow & x = -35 & & \\ & V = \left\{ -35 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (6x-6)& = & 13 \color{red}{-} (-12+x) \\\Leftrightarrow & 24x-24& = &13+12-x \\\Leftrightarrow & 24x \color{red}{-24} & = &25 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &25 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 24x+x& = &25+24 \\\Leftrightarrow & 25x& = &49 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{49}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{49}{25} & & \\ & V = \left\{ \frac{49}{25} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-2x-1)& = & -2 \color{red}{-} (-14+x) \\\Leftrightarrow & -12x-6& = &-2+14-x \\\Leftrightarrow & -12x \color{red}{-6} & = &12 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -12x+x& = &12+6 \\\Leftrightarrow & -11x& = &18 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{18}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-18}{11} & & \\ & V = \left\{ \frac{-18}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (3x-3)& = & -2 \color{red}{-} (-1+x) \\\Leftrightarrow & 6x-6& = &-2+1-x \\\Leftrightarrow & 6x \color{red}{-6} & = &-1 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 6x+x& = &-1+6 \\\Leftrightarrow & 7x& = &5 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{5}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{5}{7} & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (2x-4)& = & 8 \color{red}{+} (7+x) \\\Leftrightarrow & 12x-24& = &8+7+x \\\Leftrightarrow & 12x \color{red}{-24} & = &15 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & 12x-x& = &15+24 \\\Leftrightarrow & 11x& = &39 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{39}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{39}{11} & & \\ & V = \left\{ \frac{39}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (2x-1)& = & -10 \color{red}{+} (-6+x) \\\Leftrightarrow & 10x-5& = &-10-6+x \\\Leftrightarrow & 10x \color{red}{-5} & = &-16 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{-5} \color{blue}{+5} \color{blue}{-x} & = &-16 \color{red}{+x} \color{blue}{-x} \color{blue}{+5} \\\Leftrightarrow & 10x-x& = &-16+5 \\\Leftrightarrow & 9x& = &-11 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-11}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-11}{9} & & \\ & V = \left\{ \frac{-11}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-3x-6)& = & 2 \color{red}{-} (13-5x) \\\Leftrightarrow & -18x-36& = &2-13+5x \\\Leftrightarrow & -18x \color{red}{-36} & = &-11 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{-36} \color{blue}{+36} \color{blue}{-5x} & = &-11 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+36} \\\Leftrightarrow & -18x-5x& = &-11+36 \\\Leftrightarrow & -23x& = &25 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{25}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-25}{23} & & \\ & V = \left\{ \frac{-25}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (4x+1)& = & -1 \color{red}{-} (-8+3x) \\\Leftrightarrow & 8x+2& = &-1+8-3x \\\Leftrightarrow & 8x \color{red}{+2} & = &7 \color{red}{-3x} \\\Leftrightarrow & 8x \color{red}{+2} \color{blue}{-2} \color{blue}{+3x} & = &7 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-2} \\\Leftrightarrow & 8x+3x& = &7-2 \\\Leftrightarrow & 11x& = &5 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{5}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{5}{11} & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)