Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{5}{11})& = & -7x+\frac{8}{3} \\\Leftrightarrow & 9x-\frac{15}{11}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{297}{ \color{blue}{33} }x- \frac{45}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 297x \color{red}{-45} & = & \color{red}{-231x} +88 \\\Leftrightarrow & 297x \color{red}{-45} \color{blue}{+45} \color{blue}{+231x} & = & \color{red}{-231x} +88 \color{blue}{+231x} \color{blue}{+45} \\\Leftrightarrow & 297x+231x& = & 88+45 \\\Leftrightarrow & \color{red}{528} x& = & 133 \\\Leftrightarrow & x = \frac{133}{528} & & \\ & V = \left\{ \frac{133}{528} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{4}{9})& = & 9x+\frac{3}{7} \\\Leftrightarrow & 14x+\frac{28}{9}& = & 9x+\frac{3}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{882}{ \color{blue}{63} }x+ \frac{196}{ \color{blue}{63} })& = & (\frac{567}{ \color{blue}{63} }x+ \frac{27}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 882x \color{red}{+196} & = & \color{red}{567x} +27 \\\Leftrightarrow & 882x \color{red}{+196} \color{blue}{-196} \color{blue}{-567x} & = & \color{red}{567x} +27 \color{blue}{-567x} \color{blue}{-196} \\\Leftrightarrow & 882x-567x& = & 27-196 \\\Leftrightarrow & \color{red}{315} x& = & -169 \\\Leftrightarrow & x = \frac{-169}{315} & & \\ & V = \left\{ \frac{-169}{315} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{4}{7})& = & -6x+\frac{2}{7} \\\Leftrightarrow & 25x-\frac{20}{7}& = & -6x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{175}{ \color{blue}{7} }x- \frac{20}{ \color{blue}{7} })& = & (\frac{-42}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 175x \color{red}{-20} & = & \color{red}{-42x} +2 \\\Leftrightarrow & 175x \color{red}{-20} \color{blue}{+20} \color{blue}{+42x} & = & \color{red}{-42x} +2 \color{blue}{+42x} \color{blue}{+20} \\\Leftrightarrow & 175x+42x& = & 2+20 \\\Leftrightarrow & \color{red}{217} x& = & 22 \\\Leftrightarrow & x = \frac{22}{217} & & \\ & V = \left\{ \frac{22}{217} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{4}{5})& = & -5x+\frac{5}{7} \\\Leftrightarrow & -12x+\frac{24}{5}& = & -5x+\frac{5}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x+ \frac{168}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{25}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{+168} & = & \color{red}{-175x} +25 \\\Leftrightarrow & -420x \color{red}{+168} \color{blue}{-168} \color{blue}{+175x} & = & \color{red}{-175x} +25 \color{blue}{+175x} \color{blue}{-168} \\\Leftrightarrow & -420x+175x& = & 25-168 \\\Leftrightarrow & \color{red}{-245} x& = & -143 \\\Leftrightarrow & x = \frac{-143}{-245} & & \\\Leftrightarrow & x = \frac{143}{245} & & \\ & V = \left\{ \frac{143}{245} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{5}{7})& = & -7x+\frac{3}{7} \\\Leftrightarrow & -24x+\frac{30}{7}& = & -7x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-168}{ \color{blue}{7} }x+ \frac{30}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -168x \color{red}{+30} & = & \color{red}{-49x} +3 \\\Leftrightarrow & -168x \color{red}{+30} \color{blue}{-30} \color{blue}{+49x} & = & \color{red}{-49x} +3 \color{blue}{+49x} \color{blue}{-30} \\\Leftrightarrow & -168x+49x& = & 3-30 \\\Leftrightarrow & \color{red}{-119} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{-119} & & \\\Leftrightarrow & x = \frac{27}{119} & & \\ & V = \left\{ \frac{27}{119} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{5}{4})& = & -2x+\frac{4}{5} \\\Leftrightarrow & 21x-\frac{35}{4}& = & -2x+\frac{4}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{420}{ \color{blue}{20} }x- \frac{175}{ \color{blue}{20} })& = & (\frac{-40}{ \color{blue}{20} }x+ \frac{16}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 420x \color{red}{-175} & = & \color{red}{-40x} +16 \\\Leftrightarrow & 420x \color{red}{-175} \color{blue}{+175} \color{blue}{+40x} & = & \color{red}{-40x} +16 \color{blue}{+40x} \color{blue}{+175} \\\Leftrightarrow & 420x+40x& = & 16+175 \\\Leftrightarrow & \color{red}{460} x& = & 191 \\\Leftrightarrow & x = \frac{191}{460} & & \\ & V = \left\{ \frac{191}{460} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{2}{5})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 24x+\frac{12}{5}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{120}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 120x \color{red}{+12} & = & \color{red}{25x} +6 \\\Leftrightarrow & 120x \color{red}{+12} \color{blue}{-12} \color{blue}{-25x} & = & \color{red}{25x} +6 \color{blue}{-25x} \color{blue}{-12} \\\Leftrightarrow & 120x-25x& = & 6-12 \\\Leftrightarrow & \color{red}{95} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{95} & & \\ & V = \left\{ \frac{-6}{95} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{4}{5})& = & -7x+\frac{7}{8} \\\Leftrightarrow & 12x-\frac{12}{5}& = & -7x+\frac{7}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{480}{ \color{blue}{40} }x- \frac{96}{ \color{blue}{40} })& = & (\frac{-280}{ \color{blue}{40} }x+ \frac{35}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 480x \color{red}{-96} & = & \color{red}{-280x} +35 \\\Leftrightarrow & 480x \color{red}{-96} \color{blue}{+96} \color{blue}{+280x} & = & \color{red}{-280x} +35 \color{blue}{+280x} \color{blue}{+96} \\\Leftrightarrow & 480x+280x& = & 35+96 \\\Leftrightarrow & \color{red}{760} x& = & 131 \\\Leftrightarrow & x = \frac{131}{760} & & \\ & V = \left\{ \frac{131}{760} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{5}{8})& = & 5x+\frac{4}{3} \\\Leftrightarrow & -12x+\frac{15}{8}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-288}{ \color{blue}{24} }x+ \frac{45}{ \color{blue}{24} })& = & (\frac{120}{ \color{blue}{24} }x+ \frac{32}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -288x \color{red}{+45} & = & \color{red}{120x} +32 \\\Leftrightarrow & -288x \color{red}{+45} \color{blue}{-45} \color{blue}{-120x} & = & \color{red}{120x} +32 \color{blue}{-120x} \color{blue}{-45} \\\Leftrightarrow & -288x-120x& = & 32-45 \\\Leftrightarrow & \color{red}{-408} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-408} & & \\\Leftrightarrow & x = \frac{13}{408} & & \\ & V = \left\{ \frac{13}{408} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{3}{5})& = & 5x+\frac{10}{9} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-540}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{225}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -540x \color{red}{+108} & = & \color{red}{225x} +50 \\\Leftrightarrow & -540x \color{red}{+108} \color{blue}{-108} \color{blue}{-225x} & = & \color{red}{225x} +50 \color{blue}{-225x} \color{blue}{-108} \\\Leftrightarrow & -540x-225x& = & 50-108 \\\Leftrightarrow & \color{red}{-765} x& = & -58 \\\Leftrightarrow & x = \frac{-58}{-765} & & \\\Leftrightarrow & x = \frac{58}{765} & & \\ & V = \left\{ \frac{58}{765} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{4}{11})& = & -5x+\frac{3}{2} \\\Leftrightarrow & -4x+\frac{8}{11}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-88}{ \color{blue}{22} }x+ \frac{16}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -88x \color{red}{+16} & = & \color{red}{-110x} +33 \\\Leftrightarrow & -88x \color{red}{+16} \color{blue}{-16} \color{blue}{+110x} & = & \color{red}{-110x} +33 \color{blue}{+110x} \color{blue}{-16} \\\Leftrightarrow & -88x+110x& = & 33-16 \\\Leftrightarrow & \color{red}{22} x& = & 17 \\\Leftrightarrow & x = \frac{17}{22} & & \\ & V = \left\{ \frac{17}{22} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{3}{5})& = & -5x+\frac{3}{4} \\\Leftrightarrow & -9x-\frac{9}{5}& = & -5x+\frac{3}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-180}{ \color{blue}{20} }x- \frac{36}{ \color{blue}{20} })& = & (\frac{-100}{ \color{blue}{20} }x+ \frac{15}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -180x \color{red}{-36} & = & \color{red}{-100x} +15 \\\Leftrightarrow & -180x \color{red}{-36} \color{blue}{+36} \color{blue}{+100x} & = & \color{red}{-100x} +15 \color{blue}{+100x} \color{blue}{+36} \\\Leftrightarrow & -180x+100x& = & 15+36 \\\Leftrightarrow & \color{red}{-80} x& = & 51 \\\Leftrightarrow & x = \frac{51}{-80} & & \\\Leftrightarrow & x = \frac{-51}{80} & & \\ & V = \left\{ \frac{-51}{80} \right\} & \\\end{align}\)