Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (3x+2)& = & 4 \color{red}{-} (-14+x) \\\Leftrightarrow & 12x+8& = &4+14-x \\\Leftrightarrow & 12x \color{red}{+8} & = &18 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &18 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & 12x+x& = &18-8 \\\Leftrightarrow & 13x& = &10 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{10}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{10}{13} & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (3x-3)& = & 12 \color{red}{+} (9+4x) \\\Leftrightarrow & 9x-9& = &12+9+4x \\\Leftrightarrow & 9x \color{red}{-9} & = &21 \color{red}{+4x} \\\Leftrightarrow & 9x \color{red}{-9} \color{blue}{+9} \color{blue}{-4x} & = &21 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+9} \\\Leftrightarrow & 9x-4x& = &21+9 \\\Leftrightarrow & 5x& = &30 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{30}{ \color{red}{5} } \\\Leftrightarrow & x = 6 & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (3x+3)& = & -14 \color{red}{+} (-9+x) \\\Leftrightarrow & 9x+9& = &-14-9+x \\\Leftrightarrow & 9x \color{red}{+9} & = &-23 \color{red}{+x} \\\Leftrightarrow & 9x \color{red}{+9} \color{blue}{-9} \color{blue}{-x} & = &-23 \color{red}{+x} \color{blue}{-x} \color{blue}{-9} \\\Leftrightarrow & 9x-x& = &-23-9 \\\Leftrightarrow & 8x& = &-32 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{-32}{ \color{red}{8} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (5x-1)& = & -10 \color{red}{+} (-10+3x) \\\Leftrightarrow & 25x-5& = &-10-10+3x \\\Leftrightarrow & 25x \color{red}{-5} & = &-20 \color{red}{+3x} \\\Leftrightarrow & 25x \color{red}{-5} \color{blue}{+5} \color{blue}{-3x} & = &-20 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+5} \\\Leftrightarrow & 25x-3x& = &-20+5 \\\Leftrightarrow & 22x& = &-15 \\\Leftrightarrow & \frac{22x}{ \color{red}{22} }& = &\frac{-15}{ \color{red}{22} } \\\Leftrightarrow & x = \frac{-15}{22} & & \\ & V = \left\{ \frac{-15}{22} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-6x+2)& = & 5 \color{red}{-} (12+x) \\\Leftrightarrow & -24x+8& = &5-12-x \\\Leftrightarrow & -24x \color{red}{+8} & = &-7 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & -24x+x& = &-7-8 \\\Leftrightarrow & -23x& = &-15 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-15}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{15}{23} & & \\ & V = \left\{ \frac{15}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (x+6)& = & 8 \color{red}{+} (9-5x) \\\Leftrightarrow & 3x+18& = &8+9-5x \\\Leftrightarrow & 3x \color{red}{+18} & = &17 \color{red}{-5x} \\\Leftrightarrow & 3x \color{red}{+18} \color{blue}{-18} \color{blue}{+5x} & = &17 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-18} \\\Leftrightarrow & 3x+5x& = &17-18 \\\Leftrightarrow & 8x& = &-1 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{-1}{ \color{red}{8} } \\\Leftrightarrow & x = \frac{-1}{8} & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-5x+4)& = & -13 \color{red}{+} (-1+x) \\\Leftrightarrow & -20x+16& = &-13-1+x \\\Leftrightarrow & -20x \color{red}{+16} & = &-14 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+16} \color{blue}{-16} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{-16} \\\Leftrightarrow & -20x-x& = &-14-16 \\\Leftrightarrow & -21x& = &-30 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-30}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{10}{7} & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-5x-6)& = & -8 \color{red}{-} (-2+x) \\\Leftrightarrow & -30x-36& = &-8+2-x \\\Leftrightarrow & -30x \color{red}{-36} & = &-6 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & -30x+x& = &-6+36 \\\Leftrightarrow & -29x& = &30 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{30}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-30}{29} & & \\ & V = \left\{ \frac{-30}{29} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-5x-3)& = & 3 \color{red}{-} (7+x) \\\Leftrightarrow & -20x-12& = &3-7-x \\\Leftrightarrow & -20x \color{red}{-12} & = &-4 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -20x+x& = &-4+12 \\\Leftrightarrow & -19x& = &8 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{8}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-8}{19} & & \\ & V = \left\{ \frac{-8}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-3x+5)& = & 2 \color{red}{-} (6+x) \\\Leftrightarrow & -6x+10& = &2-6-x \\\Leftrightarrow & -6x \color{red}{+10} & = &-4 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & -6x+x& = &-4-10 \\\Leftrightarrow & -5x& = &-14 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-14}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{14}{5} & & \\ & V = \left\{ \frac{14}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-3x+4)& = & 13 \color{red}{+} (6-2x) \\\Leftrightarrow & -9x+12& = &13+6-2x \\\Leftrightarrow & -9x \color{red}{+12} & = &19 \color{red}{-2x} \\\Leftrightarrow & -9x \color{red}{+12} \color{blue}{-12} \color{blue}{+2x} & = &19 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-12} \\\Leftrightarrow & -9x+2x& = &19-12 \\\Leftrightarrow & -7x& = &7 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{7}{ \color{red}{-7} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-x+7)& = & -12 \color{red}{-} (10+x) \\\Leftrightarrow & -4x+28& = &-12-10-x \\\Leftrightarrow & -4x \color{red}{+28} & = &-22 \color{red}{-x} \\\Leftrightarrow & -4x \color{red}{+28} \color{blue}{-28} \color{blue}{+x} & = &-22 \color{red}{-x} \color{blue}{+x} \color{blue}{-28} \\\Leftrightarrow & -4x+x& = &-22-28 \\\Leftrightarrow & -3x& = &-50 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-50}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{50}{3} & & \\ & V = \left\{ \frac{50}{3} \right\} & \\\end{align}\)