Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{2}{3})& = & 3x+\frac{10}{3} \\\Leftrightarrow & 14x+\frac{14}{3}& = & 3x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{42}{ \color{blue}{3} }x+ \frac{14}{ \color{blue}{3} })& = & (\frac{9}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 42x \color{red}{+14} & = & \color{red}{9x} +10 \\\Leftrightarrow & 42x \color{red}{+14} \color{blue}{-14} \color{blue}{-9x} & = & \color{red}{9x} +10 \color{blue}{-9x} \color{blue}{-14} \\\Leftrightarrow & 42x-9x& = & 10-14 \\\Leftrightarrow & \color{red}{33} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{33} & & \\ & V = \left\{ \frac{-4}{33} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{5}{11})& = & 5x+\frac{8}{7} \\\Leftrightarrow & 12x-\frac{15}{11}& = & 5x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x- \frac{105}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{-105} & = & \color{red}{385x} +88 \\\Leftrightarrow & 924x \color{red}{-105} \color{blue}{+105} \color{blue}{-385x} & = & \color{red}{385x} +88 \color{blue}{-385x} \color{blue}{+105} \\\Leftrightarrow & 924x-385x& = & 88+105 \\\Leftrightarrow & \color{red}{539} x& = & 193 \\\Leftrightarrow & x = \frac{193}{539} & & \\ & V = \left\{ \frac{193}{539} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{3}{11})& = & -9x+\frac{10}{7} \\\Leftrightarrow & 10x-\frac{6}{11}& = & -9x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x- \frac{42}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{-42} & = & \color{red}{-693x} +110 \\\Leftrightarrow & 770x \color{red}{-42} \color{blue}{+42} \color{blue}{+693x} & = & \color{red}{-693x} +110 \color{blue}{+693x} \color{blue}{+42} \\\Leftrightarrow & 770x+693x& = & 110+42 \\\Leftrightarrow & \color{red}{1463} x& = & 152 \\\Leftrightarrow & x = \frac{152}{1463} & & \\\Leftrightarrow & x = \frac{8}{77} & & \\ & V = \left\{ \frac{8}{77} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{2}{3})& = & -6x+\frac{6}{11} \\\Leftrightarrow & -28x-\frac{14}{3}& = & -6x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-924}{ \color{blue}{33} }x- \frac{154}{ \color{blue}{33} })& = & (\frac{-198}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -924x \color{red}{-154} & = & \color{red}{-198x} +18 \\\Leftrightarrow & -924x \color{red}{-154} \color{blue}{+154} \color{blue}{+198x} & = & \color{red}{-198x} +18 \color{blue}{+198x} \color{blue}{+154} \\\Leftrightarrow & -924x+198x& = & 18+154 \\\Leftrightarrow & \color{red}{-726} x& = & 172 \\\Leftrightarrow & x = \frac{172}{-726} & & \\\Leftrightarrow & x = \frac{-86}{363} & & \\ & V = \left\{ \frac{-86}{363} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{3}{7})& = & 3x+\frac{10}{9} \\\Leftrightarrow & -20x-\frac{12}{7}& = & 3x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1260}{ \color{blue}{63} }x- \frac{108}{ \color{blue}{63} })& = & (\frac{189}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1260x \color{red}{-108} & = & \color{red}{189x} +70 \\\Leftrightarrow & -1260x \color{red}{-108} \color{blue}{+108} \color{blue}{-189x} & = & \color{red}{189x} +70 \color{blue}{-189x} \color{blue}{+108} \\\Leftrightarrow & -1260x-189x& = & 70+108 \\\Leftrightarrow & \color{red}{-1449} x& = & 178 \\\Leftrightarrow & x = \frac{178}{-1449} & & \\\Leftrightarrow & x = \frac{-178}{1449} & & \\ & V = \left\{ \frac{-178}{1449} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{5}{3})& = & 7x+\frac{5}{6} \\\Leftrightarrow & -10x+\frac{10}{3}& = & 7x+\frac{5}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-60}{ \color{blue}{6} }x+ \frac{20}{ \color{blue}{6} })& = & (\frac{42}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -60x \color{red}{+20} & = & \color{red}{42x} +5 \\\Leftrightarrow & -60x \color{red}{+20} \color{blue}{-20} \color{blue}{-42x} & = & \color{red}{42x} +5 \color{blue}{-42x} \color{blue}{-20} \\\Leftrightarrow & -60x-42x& = & 5-20 \\\Leftrightarrow & \color{red}{-102} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{-102} & & \\\Leftrightarrow & x = \frac{5}{34} & & \\ & V = \left\{ \frac{5}{34} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{2}{7})& = & -4x+\frac{5}{7} \\\Leftrightarrow & -15x+\frac{10}{7}& = & -4x+\frac{5}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-105}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} })& = & (\frac{-28}{ \color{blue}{7} }x+ \frac{5}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -105x \color{red}{+10} & = & \color{red}{-28x} +5 \\\Leftrightarrow & -105x \color{red}{+10} \color{blue}{-10} \color{blue}{+28x} & = & \color{red}{-28x} +5 \color{blue}{+28x} \color{blue}{-10} \\\Leftrightarrow & -105x+28x& = & 5-10 \\\Leftrightarrow & \color{red}{-77} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{-77} & & \\\Leftrightarrow & x = \frac{5}{77} & & \\ & V = \left\{ \frac{5}{77} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{5}{11})& = & -9x+\frac{8}{7} \\\Leftrightarrow & 14x-\frac{35}{11}& = & -9x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1078}{ \color{blue}{77} }x- \frac{245}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1078x \color{red}{-245} & = & \color{red}{-693x} +88 \\\Leftrightarrow & 1078x \color{red}{-245} \color{blue}{+245} \color{blue}{+693x} & = & \color{red}{-693x} +88 \color{blue}{+693x} \color{blue}{+245} \\\Leftrightarrow & 1078x+693x& = & 88+245 \\\Leftrightarrow & \color{red}{1771} x& = & 333 \\\Leftrightarrow & x = \frac{333}{1771} & & \\ & V = \left\{ \frac{333}{1771} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+2)& = & 3x+\frac{9}{11} \\\Leftrightarrow & -28x-14& = & 3x+\frac{9}{11} \\ & & & \text{kgv van noemers 1 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-308}{ \color{blue}{11} }x- \frac{154}{ \color{blue}{11} })& = & (\frac{33}{ \color{blue}{11} }x+ \frac{9}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -308x \color{red}{-154} & = & \color{red}{33x} +9 \\\Leftrightarrow & -308x \color{red}{-154} \color{blue}{+154} \color{blue}{-33x} & = & \color{red}{33x} +9 \color{blue}{-33x} \color{blue}{+154} \\\Leftrightarrow & -308x-33x& = & 9+154 \\\Leftrightarrow & \color{red}{-341} x& = & 163 \\\Leftrightarrow & x = \frac{163}{-341} & & \\\Leftrightarrow & x = \frac{-163}{341} & & \\ & V = \left\{ \frac{-163}{341} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{2}{3})& = & 3x+\frac{7}{12} \\\Leftrightarrow & -14x+\frac{14}{3}& = & 3x+\frac{7}{12} \\ & & & \text{kgv van noemers 3 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-168}{ \color{blue}{12} }x+ \frac{56}{ \color{blue}{12} })& = & (\frac{36}{ \color{blue}{12} }x+ \frac{7}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -168x \color{red}{+56} & = & \color{red}{36x} +7 \\\Leftrightarrow & -168x \color{red}{+56} \color{blue}{-56} \color{blue}{-36x} & = & \color{red}{36x} +7 \color{blue}{-36x} \color{blue}{-56} \\\Leftrightarrow & -168x-36x& = & 7-56 \\\Leftrightarrow & \color{red}{-204} x& = & -49 \\\Leftrightarrow & x = \frac{-49}{-204} & & \\\Leftrightarrow & x = \frac{49}{204} & & \\ & V = \left\{ \frac{49}{204} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{3}{2})& = & -5x+\frac{2}{7} \\\Leftrightarrow & 6x-\frac{9}{2}& = & -5x+\frac{2}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{84}{ \color{blue}{14} }x- \frac{63}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{4}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 84x \color{red}{-63} & = & \color{red}{-70x} +4 \\\Leftrightarrow & 84x \color{red}{-63} \color{blue}{+63} \color{blue}{+70x} & = & \color{red}{-70x} +4 \color{blue}{+70x} \color{blue}{+63} \\\Leftrightarrow & 84x+70x& = & 4+63 \\\Leftrightarrow & \color{red}{154} x& = & 67 \\\Leftrightarrow & x = \frac{67}{154} & & \\ & V = \left\{ \frac{67}{154} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{2}{5})& = & 7x+\frac{5}{7} \\\Leftrightarrow & 30x-\frac{12}{5}& = & 7x+\frac{5}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{1050}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{25}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 1050x \color{red}{-84} & = & \color{red}{245x} +25 \\\Leftrightarrow & 1050x \color{red}{-84} \color{blue}{+84} \color{blue}{-245x} & = & \color{red}{245x} +25 \color{blue}{-245x} \color{blue}{+84} \\\Leftrightarrow & 1050x-245x& = & 25+84 \\\Leftrightarrow & \color{red}{805} x& = & 109 \\\Leftrightarrow & x = \frac{109}{805} & & \\ & V = \left\{ \frac{109}{805} \right\} & \\\end{align}\)