Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{5}{3})& = & 9x+\frac{7}{5} \\\Leftrightarrow & -8x+\frac{20}{3}& = & 9x+\frac{7}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-120}{ \color{blue}{15} }x+ \frac{100}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{21}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -120x \color{red}{+100} & = & \color{red}{135x} +21 \\\Leftrightarrow & -120x \color{red}{+100} \color{blue}{-100} \color{blue}{-135x} & = & \color{red}{135x} +21 \color{blue}{-135x} \color{blue}{-100} \\\Leftrightarrow & -120x-135x& = & 21-100 \\\Leftrightarrow & \color{red}{-255} x& = & -79 \\\Leftrightarrow & x = \frac{-79}{-255} & & \\\Leftrightarrow & x = \frac{79}{255} & & \\ & V = \left\{ \frac{79}{255} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{5}{2})& = & -5x+\frac{8}{5} \\\Leftrightarrow & -12x-\frac{15}{2}& = & -5x+\frac{8}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-120}{ \color{blue}{10} }x- \frac{75}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{16}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -120x \color{red}{-75} & = & \color{red}{-50x} +16 \\\Leftrightarrow & -120x \color{red}{-75} \color{blue}{+75} \color{blue}{+50x} & = & \color{red}{-50x} +16 \color{blue}{+50x} \color{blue}{+75} \\\Leftrightarrow & -120x+50x& = & 16+75 \\\Leftrightarrow & \color{red}{-70} x& = & 91 \\\Leftrightarrow & x = \frac{91}{-70} & & \\\Leftrightarrow & x = \frac{-13}{10} & & \\ & V = \left\{ \frac{-13}{10} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{4}{7})& = & -5x+\frac{10}{9} \\\Leftrightarrow & 18x-\frac{24}{7}& = & -5x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1134}{ \color{blue}{63} }x- \frac{216}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1134x \color{red}{-216} & = & \color{red}{-315x} +70 \\\Leftrightarrow & 1134x \color{red}{-216} \color{blue}{+216} \color{blue}{+315x} & = & \color{red}{-315x} +70 \color{blue}{+315x} \color{blue}{+216} \\\Leftrightarrow & 1134x+315x& = & 70+216 \\\Leftrightarrow & \color{red}{1449} x& = & 286 \\\Leftrightarrow & x = \frac{286}{1449} & & \\ & V = \left\{ \frac{286}{1449} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{5}{7})& = & -7x+\frac{5}{9} \\\Leftrightarrow & -10x+\frac{10}{7}& = & -7x+\frac{5}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-630}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{35}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -630x \color{red}{+90} & = & \color{red}{-441x} +35 \\\Leftrightarrow & -630x \color{red}{+90} \color{blue}{-90} \color{blue}{+441x} & = & \color{red}{-441x} +35 \color{blue}{+441x} \color{blue}{-90} \\\Leftrightarrow & -630x+441x& = & 35-90 \\\Leftrightarrow & \color{red}{-189} x& = & -55 \\\Leftrightarrow & x = \frac{-55}{-189} & & \\\Leftrightarrow & x = \frac{55}{189} & & \\ & V = \left\{ \frac{55}{189} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{5}{11})& = & -5x+\frac{3}{2} \\\Leftrightarrow & -12x-\frac{30}{11}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-264}{ \color{blue}{22} }x- \frac{60}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -264x \color{red}{-60} & = & \color{red}{-110x} +33 \\\Leftrightarrow & -264x \color{red}{-60} \color{blue}{+60} \color{blue}{+110x} & = & \color{red}{-110x} +33 \color{blue}{+110x} \color{blue}{+60} \\\Leftrightarrow & -264x+110x& = & 33+60 \\\Leftrightarrow & \color{red}{-154} x& = & 93 \\\Leftrightarrow & x = \frac{93}{-154} & & \\\Leftrightarrow & x = \frac{-93}{154} & & \\ & V = \left\{ \frac{-93}{154} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{2}{7})& = & 2x+\frac{10}{9} \\\Leftrightarrow & 15x-\frac{10}{7}& = & 2x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{945}{ \color{blue}{63} }x- \frac{90}{ \color{blue}{63} })& = & (\frac{126}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 945x \color{red}{-90} & = & \color{red}{126x} +70 \\\Leftrightarrow & 945x \color{red}{-90} \color{blue}{+90} \color{blue}{-126x} & = & \color{red}{126x} +70 \color{blue}{-126x} \color{blue}{+90} \\\Leftrightarrow & 945x-126x& = & 70+90 \\\Leftrightarrow & \color{red}{819} x& = & 160 \\\Leftrightarrow & x = \frac{160}{819} & & \\ & V = \left\{ \frac{160}{819} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{4}{7})& = & -3x+\frac{8}{9} \\\Leftrightarrow & -25x-\frac{20}{7}& = & -3x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1575}{ \color{blue}{63} }x- \frac{180}{ \color{blue}{63} })& = & (\frac{-189}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1575x \color{red}{-180} & = & \color{red}{-189x} +56 \\\Leftrightarrow & -1575x \color{red}{-180} \color{blue}{+180} \color{blue}{+189x} & = & \color{red}{-189x} +56 \color{blue}{+189x} \color{blue}{+180} \\\Leftrightarrow & -1575x+189x& = & 56+180 \\\Leftrightarrow & \color{red}{-1386} x& = & 236 \\\Leftrightarrow & x = \frac{236}{-1386} & & \\\Leftrightarrow & x = \frac{-118}{693} & & \\ & V = \left\{ \frac{-118}{693} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{5}{3})& = & 2x+\frac{2}{3} \\\Leftrightarrow & 35x+\frac{35}{3}& = & 2x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{105}{ \color{blue}{3} }x+ \frac{35}{ \color{blue}{3} })& = & (\frac{6}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 105x \color{red}{+35} & = & \color{red}{6x} +2 \\\Leftrightarrow & 105x \color{red}{+35} \color{blue}{-35} \color{blue}{-6x} & = & \color{red}{6x} +2 \color{blue}{-6x} \color{blue}{-35} \\\Leftrightarrow & 105x-6x& = & 2-35 \\\Leftrightarrow & \color{red}{99} x& = & -33 \\\Leftrightarrow & x = \frac{-33}{99} & & \\\Leftrightarrow & x = \frac{-1}{3} & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{4}{7})& = & 5x+\frac{10}{7} \\\Leftrightarrow & -24x+\frac{24}{7}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-168}{ \color{blue}{7} }x+ \frac{24}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -168x \color{red}{+24} & = & \color{red}{35x} +10 \\\Leftrightarrow & -168x \color{red}{+24} \color{blue}{-24} \color{blue}{-35x} & = & \color{red}{35x} +10 \color{blue}{-35x} \color{blue}{-24} \\\Leftrightarrow & -168x-35x& = & 10-24 \\\Leftrightarrow & \color{red}{-203} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{-203} & & \\\Leftrightarrow & x = \frac{2}{29} & & \\ & V = \left\{ \frac{2}{29} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{5}{9})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 8x+\frac{20}{9}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{360}{ \color{blue}{45} }x+ \frac{100}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 360x \color{red}{+100} & = & \color{red}{-315x} +54 \\\Leftrightarrow & 360x \color{red}{+100} \color{blue}{-100} \color{blue}{+315x} & = & \color{red}{-315x} +54 \color{blue}{+315x} \color{blue}{-100} \\\Leftrightarrow & 360x+315x& = & 54-100 \\\Leftrightarrow & \color{red}{675} x& = & -46 \\\Leftrightarrow & x = \frac{-46}{675} & & \\ & V = \left\{ \frac{-46}{675} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{5}{9})& = & 5x+\frac{8}{3} \\\Leftrightarrow & -4x+\frac{10}{9}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-36}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} })& = & (\frac{45}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -36x \color{red}{+10} & = & \color{red}{45x} +24 \\\Leftrightarrow & -36x \color{red}{+10} \color{blue}{-10} \color{blue}{-45x} & = & \color{red}{45x} +24 \color{blue}{-45x} \color{blue}{-10} \\\Leftrightarrow & -36x-45x& = & 24-10 \\\Leftrightarrow & \color{red}{-81} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-81} & & \\\Leftrightarrow & x = \frac{-14}{81} & & \\ & V = \left\{ \frac{-14}{81} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{4}{11})& = & 4x+\frac{9}{2} \\\Leftrightarrow & 15x-\frac{12}{11}& = & 4x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{330}{ \color{blue}{22} }x- \frac{24}{ \color{blue}{22} })& = & (\frac{88}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 330x \color{red}{-24} & = & \color{red}{88x} +99 \\\Leftrightarrow & 330x \color{red}{-24} \color{blue}{+24} \color{blue}{-88x} & = & \color{red}{88x} +99 \color{blue}{-88x} \color{blue}{+24} \\\Leftrightarrow & 330x-88x& = & 99+24 \\\Leftrightarrow & \color{red}{242} x& = & 123 \\\Leftrightarrow & x = \frac{123}{242} & & \\ & V = \left\{ \frac{123}{242} \right\} & \\\end{align}\)