Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{2}{3})& = & 7x+\frac{3}{11} \\\Leftrightarrow & -16x+\frac{8}{3}& = & 7x+\frac{3}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-528}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{9}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -528x \color{red}{+88} & = & \color{red}{231x} +9 \\\Leftrightarrow & -528x \color{red}{+88} \color{blue}{-88} \color{blue}{-231x} & = & \color{red}{231x} +9 \color{blue}{-231x} \color{blue}{-88} \\\Leftrightarrow & -528x-231x& = & 9-88 \\\Leftrightarrow & \color{red}{-759} x& = & -79 \\\Leftrightarrow & x = \frac{-79}{-759} & & \\\Leftrightarrow & x = \frac{79}{759} & & \\ & V = \left\{ \frac{79}{759} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{3}{8})& = & -4x+\frac{6}{7} \\\Leftrightarrow & -15x-\frac{15}{8}& = & -4x+\frac{6}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-840}{ \color{blue}{56} }x- \frac{105}{ \color{blue}{56} })& = & (\frac{-224}{ \color{blue}{56} }x+ \frac{48}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -840x \color{red}{-105} & = & \color{red}{-224x} +48 \\\Leftrightarrow & -840x \color{red}{-105} \color{blue}{+105} \color{blue}{+224x} & = & \color{red}{-224x} +48 \color{blue}{+224x} \color{blue}{+105} \\\Leftrightarrow & -840x+224x& = & 48+105 \\\Leftrightarrow & \color{red}{-616} x& = & 153 \\\Leftrightarrow & x = \frac{153}{-616} & & \\\Leftrightarrow & x = \frac{-153}{616} & & \\ & V = \left\{ \frac{-153}{616} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{2}{7})& = & -5x+\frac{9}{2} \\\Leftrightarrow & 6x-\frac{6}{7}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{84}{ \color{blue}{14} }x- \frac{12}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 84x \color{red}{-12} & = & \color{red}{-70x} +63 \\\Leftrightarrow & 84x \color{red}{-12} \color{blue}{+12} \color{blue}{+70x} & = & \color{red}{-70x} +63 \color{blue}{+70x} \color{blue}{+12} \\\Leftrightarrow & 84x+70x& = & 63+12 \\\Leftrightarrow & \color{red}{154} x& = & 75 \\\Leftrightarrow & x = \frac{75}{154} & & \\ & V = \left\{ \frac{75}{154} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{5}{11})& = & -3x+\frac{5}{7} \\\Leftrightarrow & 10x-\frac{25}{11}& = & -3x+\frac{5}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x- \frac{175}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{55}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{-175} & = & \color{red}{-231x} +55 \\\Leftrightarrow & 770x \color{red}{-175} \color{blue}{+175} \color{blue}{+231x} & = & \color{red}{-231x} +55 \color{blue}{+231x} \color{blue}{+175} \\\Leftrightarrow & 770x+231x& = & 55+175 \\\Leftrightarrow & \color{red}{1001} x& = & 230 \\\Leftrightarrow & x = \frac{230}{1001} & & \\ & V = \left\{ \frac{230}{1001} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{2}{7})& = & -2x+\frac{3}{10} \\\Leftrightarrow & 15x+\frac{10}{7}& = & -2x+\frac{3}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{1050}{ \color{blue}{70} }x+ \frac{100}{ \color{blue}{70} })& = & (\frac{-140}{ \color{blue}{70} }x+ \frac{21}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 1050x \color{red}{+100} & = & \color{red}{-140x} +21 \\\Leftrightarrow & 1050x \color{red}{+100} \color{blue}{-100} \color{blue}{+140x} & = & \color{red}{-140x} +21 \color{blue}{+140x} \color{blue}{-100} \\\Leftrightarrow & 1050x+140x& = & 21-100 \\\Leftrightarrow & \color{red}{1190} x& = & -79 \\\Leftrightarrow & x = \frac{-79}{1190} & & \\ & V = \left\{ \frac{-79}{1190} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{4}{5})& = & -7x+\frac{7}{11} \\\Leftrightarrow & 12x-\frac{12}{5}& = & -7x+\frac{7}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{35}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{-132} & = & \color{red}{-385x} +35 \\\Leftrightarrow & 660x \color{red}{-132} \color{blue}{+132} \color{blue}{+385x} & = & \color{red}{-385x} +35 \color{blue}{+385x} \color{blue}{+132} \\\Leftrightarrow & 660x+385x& = & 35+132 \\\Leftrightarrow & \color{red}{1045} x& = & 167 \\\Leftrightarrow & x = \frac{167}{1045} & & \\ & V = \left\{ \frac{167}{1045} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{3}{5})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 12x-\frac{9}{5}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{60}{ \color{blue}{5} }x- \frac{9}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 60x \color{red}{-9} & = & \color{red}{25x} +6 \\\Leftrightarrow & 60x \color{red}{-9} \color{blue}{+9} \color{blue}{-25x} & = & \color{red}{25x} +6 \color{blue}{-25x} \color{blue}{+9} \\\Leftrightarrow & 60x-25x& = & 6+9 \\\Leftrightarrow & \color{red}{35} x& = & 15 \\\Leftrightarrow & x = \frac{15}{35} & & \\\Leftrightarrow & x = \frac{3}{7} & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{3}{7})& = & -9x+\frac{3}{10} \\\Leftrightarrow & -8x+\frac{6}{7}& = & -9x+\frac{3}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-560}{ \color{blue}{70} }x+ \frac{60}{ \color{blue}{70} })& = & (\frac{-630}{ \color{blue}{70} }x+ \frac{21}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -560x \color{red}{+60} & = & \color{red}{-630x} +21 \\\Leftrightarrow & -560x \color{red}{+60} \color{blue}{-60} \color{blue}{+630x} & = & \color{red}{-630x} +21 \color{blue}{+630x} \color{blue}{-60} \\\Leftrightarrow & -560x+630x& = & 21-60 \\\Leftrightarrow & \color{red}{70} x& = & -39 \\\Leftrightarrow & x = \frac{-39}{70} & & \\ & V = \left\{ \frac{-39}{70} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{4}{5})& = & -5x+\frac{10}{9} \\\Leftrightarrow & 18x-\frac{24}{5}& = & -5x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{810}{ \color{blue}{45} }x- \frac{216}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 810x \color{red}{-216} & = & \color{red}{-225x} +50 \\\Leftrightarrow & 810x \color{red}{-216} \color{blue}{+216} \color{blue}{+225x} & = & \color{red}{-225x} +50 \color{blue}{+225x} \color{blue}{+216} \\\Leftrightarrow & 810x+225x& = & 50+216 \\\Leftrightarrow & \color{red}{1035} x& = & 266 \\\Leftrightarrow & x = \frac{266}{1035} & & \\ & V = \left\{ \frac{266}{1035} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{4}{7})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -30x+\frac{24}{7}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-1050}{ \color{blue}{35} }x+ \frac{120}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -1050x \color{red}{+120} & = & \color{red}{-245x} +42 \\\Leftrightarrow & -1050x \color{red}{+120} \color{blue}{-120} \color{blue}{+245x} & = & \color{red}{-245x} +42 \color{blue}{+245x} \color{blue}{-120} \\\Leftrightarrow & -1050x+245x& = & 42-120 \\\Leftrightarrow & \color{red}{-805} x& = & -78 \\\Leftrightarrow & x = \frac{-78}{-805} & & \\\Leftrightarrow & x = \frac{78}{805} & & \\ & V = \left\{ \frac{78}{805} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{3}{5})& = & 7x+\frac{6}{5} \\\Leftrightarrow & 30x+\frac{18}{5}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{150}{ \color{blue}{5} }x+ \frac{18}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 150x \color{red}{+18} & = & \color{red}{35x} +6 \\\Leftrightarrow & 150x \color{red}{+18} \color{blue}{-18} \color{blue}{-35x} & = & \color{red}{35x} +6 \color{blue}{-35x} \color{blue}{-18} \\\Leftrightarrow & 150x-35x& = & 6-18 \\\Leftrightarrow & \color{red}{115} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{115} & & \\ & V = \left\{ \frac{-12}{115} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{4}{11})& = & -3x+\frac{9}{10} \\\Leftrightarrow & 20x-\frac{16}{11}& = & -3x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{2200}{ \color{blue}{110} }x- \frac{160}{ \color{blue}{110} })& = & (\frac{-330}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 2200x \color{red}{-160} & = & \color{red}{-330x} +99 \\\Leftrightarrow & 2200x \color{red}{-160} \color{blue}{+160} \color{blue}{+330x} & = & \color{red}{-330x} +99 \color{blue}{+330x} \color{blue}{+160} \\\Leftrightarrow & 2200x+330x& = & 99+160 \\\Leftrightarrow & \color{red}{2530} x& = & 259 \\\Leftrightarrow & x = \frac{259}{2530} & & \\ & V = \left\{ \frac{259}{2530} \right\} & \\\end{align}\)