Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-6x+6)& = & 4 \color{red}{-} (-1-5x) \\\Leftrightarrow & -36x+36& = &4+1+5x \\\Leftrightarrow & -36x \color{red}{+36} & = &5 \color{red}{+5x} \\\Leftrightarrow & -36x \color{red}{+36} \color{blue}{-36} \color{blue}{-5x} & = &5 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-36} \\\Leftrightarrow & -36x-5x& = &5-36 \\\Leftrightarrow & -41x& = &-31 \\\Leftrightarrow & \frac{-41x}{ \color{red}{-41} }& = &\frac{-31}{ \color{red}{-41} } \\\Leftrightarrow & x = \frac{31}{41} & & \\ & V = \left\{ \frac{31}{41} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (6x-2)& = & 5 \color{red}{+} (-3+x) \\\Leftrightarrow & 30x-10& = &5-3+x \\\Leftrightarrow & 30x \color{red}{-10} & = &2 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & 30x-x& = &2+10 \\\Leftrightarrow & 29x& = &12 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{12}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{12}{29} & & \\ & V = \left\{ \frac{12}{29} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (x-1)& = & 12 \color{red}{-} (-6-2x) \\\Leftrightarrow & 5x-5& = &12+6+2x \\\Leftrightarrow & 5x \color{red}{-5} & = &18 \color{red}{+2x} \\\Leftrightarrow & 5x \color{red}{-5} \color{blue}{+5} \color{blue}{-2x} & = &18 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+5} \\\Leftrightarrow & 5x-2x& = &18+5 \\\Leftrightarrow & 3x& = &23 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{23}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{23}{3} & & \\ & V = \left\{ \frac{23}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (x-1)& = & -4 \color{red}{-} (13-5x) \\\Leftrightarrow & 6x-6& = &-4-13+5x \\\Leftrightarrow & 6x \color{red}{-6} & = &-17 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{-6} \color{blue}{+6} \color{blue}{-5x} & = &-17 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+6} \\\Leftrightarrow & 6x-5x& = &-17+6 \\\Leftrightarrow & x& = &-11 \\ & V = \left\{ -11 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (5x+5)& = & -6 \color{red}{-} (11+3x) \\\Leftrightarrow & 20x+20& = &-6-11-3x \\\Leftrightarrow & 20x \color{red}{+20} & = &-17 \color{red}{-3x} \\\Leftrightarrow & 20x \color{red}{+20} \color{blue}{-20} \color{blue}{+3x} & = &-17 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-20} \\\Leftrightarrow & 20x+3x& = &-17-20 \\\Leftrightarrow & 23x& = &-37 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-37}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-37}{23} & & \\ & V = \left\{ \frac{-37}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-6x+5)& = & 14 \color{red}{+} (15+x) \\\Leftrightarrow & -30x+25& = &14+15+x \\\Leftrightarrow & -30x \color{red}{+25} & = &29 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+25} \color{blue}{-25} \color{blue}{-x} & = &29 \color{red}{+x} \color{blue}{-x} \color{blue}{-25} \\\Leftrightarrow & -30x-x& = &29-25 \\\Leftrightarrow & -31x& = &4 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{4}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-4}{31} & & \\ & V = \left\{ \frac{-4}{31} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (2x-5)& = & 4 \color{red}{+} (2+x) \\\Leftrightarrow & 12x-30& = &4+2+x \\\Leftrightarrow & 12x \color{red}{-30} & = &6 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 12x-x& = &6+30 \\\Leftrightarrow & 11x& = &36 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{36}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{36}{11} & & \\ & V = \left\{ \frac{36}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-6x+7)& = & -5 \color{red}{-} (10+x) \\\Leftrightarrow & -36x+42& = &-5-10-x \\\Leftrightarrow & -36x \color{red}{+42} & = &-15 \color{red}{-x} \\\Leftrightarrow & -36x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &-15 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & -36x+x& = &-15-42 \\\Leftrightarrow & -35x& = &-57 \\\Leftrightarrow & \frac{-35x}{ \color{red}{-35} }& = &\frac{-57}{ \color{red}{-35} } \\\Leftrightarrow & x = \frac{57}{35} & & \\ & V = \left\{ \frac{57}{35} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (3x+2)& = & 12 \color{red}{-} (5+x) \\\Leftrightarrow & 12x+8& = &12-5-x \\\Leftrightarrow & 12x \color{red}{+8} & = &7 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & 12x+x& = &7-8 \\\Leftrightarrow & 13x& = &-1 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-1}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-1}{13} & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (6x-4)& = & -1 \color{red}{-} (-5+x) \\\Leftrightarrow & 36x-24& = &-1+5-x \\\Leftrightarrow & 36x \color{red}{-24} & = &4 \color{red}{-x} \\\Leftrightarrow & 36x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 36x+x& = &4+24 \\\Leftrightarrow & 37x& = &28 \\\Leftrightarrow & \frac{37x}{ \color{red}{37} }& = &\frac{28}{ \color{red}{37} } \\\Leftrightarrow & x = \frac{28}{37} & & \\ & V = \left\{ \frac{28}{37} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (6x-3)& = & -8 \color{red}{-} (14+x) \\\Leftrightarrow & 18x-9& = &-8-14-x \\\Leftrightarrow & 18x \color{red}{-9} & = &-22 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{-9} \color{blue}{+9} \color{blue}{+x} & = &-22 \color{red}{-x} \color{blue}{+x} \color{blue}{+9} \\\Leftrightarrow & 18x+x& = &-22+9 \\\Leftrightarrow & 19x& = &-13 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-13}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-13}{19} & & \\ & V = \left\{ \frac{-13}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (x+1)& = & -5 \color{red}{+} (-3+x) \\\Leftrightarrow & 3x+3& = &-5-3+x \\\Leftrightarrow & 3x \color{red}{+3} & = &-8 \color{red}{+x} \\\Leftrightarrow & 3x \color{red}{+3} \color{blue}{-3} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{-3} \\\Leftrightarrow & 3x-x& = &-8-3 \\\Leftrightarrow & 2x& = &-11 \\\Leftrightarrow & \frac{2x}{ \color{red}{2} }& = &\frac{-11}{ \color{red}{2} } \\\Leftrightarrow & x = \frac{-11}{2} & & \\ & V = \left\{ \frac{-11}{2} \right\} & \\\end{align}\)